Theorem bi23imp13 38697

Description: 3imp 1256 with middle implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017.)

Hypothesis

Ref	Expression
bi23imp13.1	|- ( ph -> ( ps <-> ( ch -> th ) ) )

Assertion

Ref	Expression
bi23imp13	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem bi23imp13

Step	Hyp	Ref	Expression
1		bi23imp13.1	. . 3 |- ( ph -> ( ps <-> ( ch -> th ) ) )
2	1	biimpd 219	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	3imp 1256	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   <-> wb 196   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  bi12imp3  38700