jumping power from single switch to dual switch (independent)


A friend and I ran a new circuit from the panel (15A breaker) for a switched vanity light and GFCI outlet in the bathroom. I am planning to connect an exhaust fan/light (not over tub) taking power from the new circuit via the vanity light switch and connecting to a dual switch (top - fan, bottom - light) the light and fan will be independent of each other.
I have the following: working: main switch/vanity light: hot (black) feed to switch H1, hot (black) feed to light from switch H2, grounds connected and terminated on switch G1, neutrals connected.
in progress: fan: separate line (blue to black - hot, white to white - neutral) ground on fan housing, leads in switch box ready for dual switch connection. light: separate line (black to black - hot, white to white - neutral) ground on fan housing, leads in switch box ready for dual switch connection.
My question is how do I complete the wiring for the dual switch (fan and ligh)t? I would like to use the common hot and keep the tab (on switch) in place to save room in the switch box.
My guess is that I can jump the hot lead from main switch to the dual switch, jump the neutrals to the dual switch and connect the common grounds. Something tells me that this is too simple based on the wiring for the main switch/vanity light. Any feedback is greatly appreciated.
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Your combination "two single pole switches" should have the hot on the bridged side with tab in place, and the "load" wires to the fan and light on the other side. The neutrals don't go on the switch, just wire nutted together. FWIW, it doesn't meet current NEC to do this on a 15 amp circuit. It would need to be 20

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