Theorem abai 770

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 325	. 2 |- (ph -> (ps <-> (ph -> ps)))
2	1	pm5.32i 618	1 |- ((ph /\ ps) <-> (ph /\ (ph -> ps)))

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  eu2  2229  2eu6  2289  dfss4  3489