To follow on from the wise words of
MarkerInbound, most modern aircraft have a VLS (V, Low Speed) displayed on the speed tape, or "eyebrows" on the ADI showing maximum pitch angle, all of these are supplied by the Angle of Attack vanes, independant of the manometric system. Staying comfortably above the VLS, and comfortably below the "eyebrows" should keep you safe.
(Well I lied slightly, they do refer to Static Pressure to compute the stall angle of attack at very high altitudes, but you were referring to the "After Takeoff" case).
After you've landed, buy a lottery ticket, the odds in favour of a dual ADC failure plus a pneumatic standby IAS failure are billions to one against.
Regards,
Old Smokey