Theorem e1bir

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

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

Proof

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