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Theorem a1bi 242
Description: Inference introducing a theorem as an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 11-Nov-2012.)
Hypothesis
Ref Expression
a1bi.1  |-  ph
Assertion
Ref Expression
a1bi  |-  ( ps  <->  (
ph  ->  ps ) )

Proof of Theorem a1bi
StepHypRef Expression
1 a1bi.1 . 2  |-  ph
2 biimt 240 . 2  |-  ( ph  ->  ( ps  <->  ( ph  ->  ps ) ) )
31, 2ax-mp 5 1  |-  ( ps  <->  (
ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> 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:  mt2bi  674  truimfal  1389  equsal  1706  equveli  1733  ralv  2706  relop  4697
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