Theorem bi33imp12 38696

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

Hypothesis

Ref	Expression
bi33imp12.1	|- ( ph -> ( ps -> ( ch <-> th ) ) )

Assertion

Ref	Expression
bi33imp12	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem bi33imp12

Step	Hyp	Ref	Expression
1		bi33imp12.1	. . 3 |- ( ph -> ( ps -> ( ch <-> th ) ) )
2		biimp 205	. . 3 |- ( ( ch <-> th ) -> ( ch -> th ) )
3	1, 2	syl6 35	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
4	3	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:  bi13imp2  38699