Theorem e3bi 38965

Description: Biconditional form of e3 38964. syl8ib 246 is e3bi 38965 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e3bi.1	|- (. ph ,. ps ,. ch ->. th ).
e3bi.2	|- ( th <-> ta )

Assertion

Ref	Expression
e3bi	|- (. ph ,. ps ,. ch ->. ta ).

Proof of Theorem e3bi

Step	Hyp	Ref	Expression
1		e3bi.1	. 2 |- (. ph ,. ps ,. ch ->. th ).
2		e3bi.2	. . 3 |- ( th <-> ta )
3	2	biimpi 206	. 2 |- ( th -> ta )
4	1, 3	e3 38964	1 |- (. ph ,. ps ,. ch ->. ta ).

Syntax hints:   <-> wb 196   (.wvd3 38803

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  df-vd3 38806

This theorem is referenced by:  en3lplem2VD  39079