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Theorem bianfd 892
Description: A wff conjoined with falsehood is false. (Contributed by NM, 27-Mar-1995.) (Proof shortened by Wolf Lammen, 5-Nov-2013.)
Hypothesis
Ref Expression
bianfd.1  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
bianfd  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ch ) ) )

Proof of Theorem bianfd
StepHypRef Expression
1 bianfd.1 . 2  |-  ( ph  ->  -.  ps )
21intnanrd 883 . 2  |-  ( ph  ->  -.  ( ps  /\  ch ) )
31, 22falsed 340 1  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  eueq2  2939  eueq3  2940
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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