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Theorem abai 772
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
StepHypRef Expression
1 biimt 327 . 2  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
21pm5.32i 620 1  |-  ( (
ph  /\  ps )  <->  (
ph  /\  ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ wa 360
This theorem is referenced by:  sbequ8  1665  eu2  2312  2eu6  2372  dfss4  3560  tfrlem2  6666  choc0  22859
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 179  df-an 362
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