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Metamath Proof Explorer

Theorem e1bi

Description: Biconditional form of e1a . sylib is e1bi without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1bi.1	\|- (. ph ->. ps ).
	e1bi.2	\|- ( ps <-> ch )
Assertion	e1bi	\|- (. ph ->. ch ).

Proof

Step	Hyp	Ref	Expression
1		e1bi.1	\|- (. ph ->. ps ).
2		e1bi.2	\|- ( ps <-> ch )
3	2	biimpi	\|- ( ps -> ch )
4	1 3	e1a	\|- (. ph ->. ch ).