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Theorem bianfi 891
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 880 . 2  |-  -.  ( ps  /\  ph )
31, 22false 339 1  |-  ( ph  <->  ( ps  /\  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    /\ wa 358
This theorem is referenced by:  in0  3480  opthprc  4736  ind1a  23604
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
  Copyright terms: Public domain W3C validator