Theorem abai 836

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 350	. 2 |- ( ph -> ( ps <-> ( ph -> ps ) ) )
2	1	pm5.32i 669	1 |- ( ( ph /\ ps ) <-> ( ph /\ ( ph -> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  exintrbi  1818  sbequ8  1885  eu5  2496  r19.29imd  3074  dfss4  3858  choc0  28185