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Theorem bianfi 932
Description: A wff conjoined with falsehood is false. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Hypothesis
Ref Expression
bianfi.1  |-  -.  ph
Assertion
Ref Expression
bianfi  |-  ( ph  <->  ( ps  /\  ph )
)

Proof of Theorem bianfi
StepHypRef Expression
1 bianfi.1 . 2  |-  -.  ph
21intnan 915 . 2  |-  -.  ( ps  /\  ph )
31, 22false 691 1  |-  ( ph  <->  ( ps  /\  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  in0  3401  opthprc  4597
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