Theorem dfbi2

Description: A theorem similar to the standard definition of the biconditional. Definition of Margaris p. 49. (Contributed by NM, 24-Jan-1993)

	Ref	Expression
Assertion	dfbi2	|- ( ( ph <-> ps ) <-> ( ( ph -> ps ) /\ ( ps -> ph ) ) )

Proof

Step	Hyp	Ref	Expression
1		dfbi1	|- ( ( ph <-> ps ) <-> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) )
2		df-an	|- ( ( ( ph -> ps ) /\ ( ps -> ph ) ) <-> -. ( ( ph -> ps ) -> -. ( ps -> ph ) ) )
3	1 2	bitr4i	|- ( ( ph <-> ps ) <-> ( ( ph -> ps ) /\ ( ps -> ph ) ) )