Theorem e3bi

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

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

Proof

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