Theorem 3impexpbicomi 1415

Description: Deduction form of 3impexpbicom 1414. (Contributed by Alan Sare, 31-Dec-2011.)

Hypothesis

Ref	Expression
3impexpbicomi.1	|- ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )

Assertion

Ref	Expression
3impexpbicomi	|- ( ph -> ( ps -> ( ch -> ( ta <-> th ) ) ) )

Proof of Theorem 3impexpbicomi

Step	Hyp	Ref	Expression
1		3impexpbicomi.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )
2	1	bicomd 140	. 2 |- ( ( ph /\ ps /\ ch ) -> ( ta <-> th ) )
3	2	3exp 1180	1 |- ( ph -> ( ps -> ( ch -> ( ta <-> th ) ) ) )

Syntax hints:   -> wi 4   <-> wb 104   /\ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by: (None)