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Theorem abai 549
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 240 . 2  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
21pm5.32i 449 1  |-  ( (
ph  /\  ps )  <->  (
ph  /\  ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  eu2  2043  dfss4st  3309
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