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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
StepHypRef Expression
1 biimt 325 . 2  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
21pm5.32i 618 1  |-  ( (
ph  /\  ps )  <->  (
ph  /\  ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  eu2  2168  2eu6  2228  dfss4  3403  tfrlem2  6392  choc0  21905
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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