Theorem abai 560

Description: Introduce one conjunct as an antecedent to the other. "abai" stands for "and, biconditional, and, implication". (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)

Assertion

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

Proof of Theorem abai

Step	Hyp	Ref	Expression
1		biimt 241	. 2 |- ( ph -> ( ps <-> ( ph -> ps ) ) )
2	1	pm5.32i 454	1 |- ( ( ph /\ ps ) <-> ( ph /\ ( ph -> ps ) ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  eu2  2089  dfss4st  3396