Theorem e1bir 38855

Description: Right biconditional form of e1a 38852. sylibr 224 is e1bir 38855 without virtual deductions. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e1bir.1	|- (. ph ->. ps ).
e1bir.2	|- ( ch <-> ps )

Assertion

Ref	Expression
e1bir	|- (. ph ->. ch ).

Proof of Theorem e1bir

Step	Hyp	Ref	Expression
1		e1bir.1	. 2 |- (. ph ->. ps ).
2		e1bir.2	. . 3 |- ( ch <-> ps )
3	2	biimpri 218	. 2 |- ( ps -> ch )
4	1, 3	e1a 38852	1 |- (. ph ->. ch ).

Syntax hints:   <-> wb 196   (.wvd1 38785

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-vd1 38786

This theorem is referenced by:  en3lplem2VD  39079