Theorem pm5.1 565

Description: Two propositions are equivalent if they are both true. Theorem *5.1 of [WhiteheadRussell] p. 123. (Contributed by NM, 21-May-1994.)

Assertion

Ref	Expression
pm5.1	|- ( ( ph /\ ps ) -> ( ph <-> ps ) )

Proof of Theorem pm5.1

Step	Hyp	Ref	Expression
1		pm5.501 242	. 2 |- ( ph -> ( ps <-> ( ph <-> ps ) ) )
2	1	biimpa 290	1 |- ( ( ph /\ ps ) -> ( ph <-> ps ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm5.35  859  ssconb  3105