Theorem ee3bir 38709

Description: Right-biconditional form of e3 38964 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 22-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee3bir.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee3bir.2	|- ( ta <-> th )

Assertion

Ref	Expression
ee3bir	|- ( ph -> ( ps -> ( ch -> ta ) ) )

Proof of Theorem ee3bir

Step	Hyp	Ref	Expression
1		ee3bir.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee3bir.2	. . 3 |- ( ta <-> th )
3	2	biimpri 218	. 2 |- ( th -> ta )
4	1, 3	syl8 76	1 |- ( ph -> ( ps -> ( ch -> ta ) ) )

Syntax hints:   -> wi 4   <-> wb 196

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

This theorem is referenced by: (None)