Metamath Proof Explorer


Theorem coinflipuniv

Description: The universe of our coin-flip probability is { H , T } . (Contributed by Thierry Arnoux, 15-Jan-2017)

Ref Expression
Hypotheses coinflip.h H V
coinflip.t T V
coinflip.th H T
coinflip.2 P = . 𝒫 H T fc ÷ 2
coinflip.3 X = H 1 T 0
Assertion coinflipuniv dom P = H T

Proof

Step Hyp Ref Expression
1 coinflip.h H V
2 coinflip.t T V
3 coinflip.th H T
4 coinflip.2 P = . 𝒫 H T fc ÷ 2
5 coinflip.3 X = H 1 T 0
6 1 2 3 4 5 coinflipspace dom P = 𝒫 H T
7 6 unieqi dom P = 𝒫 H T
8 unipw 𝒫 H T = H T
9 7 8 eqtri dom P = H T