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Theorem intnanrd 900
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005.)
Hypothesis
Ref Expression
intnand.1  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
intnanrd  |-  ( ph  ->  -.  ( ps  /\  ch ) )

Proof of Theorem intnanrd
StepHypRef Expression
1 intnand.1 . 2  |-  ( ph  ->  -.  ps )
2 simpl 108 . 2  |-  ( ( ps  /\  ch )  ->  ps )
31, 2nsyl 600 1  |-  ( ph  ->  -.  ( ps  /\  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 586  ax-in2 587
This theorem is referenced by:  dcan  901  bianfd  915  frecabcl  6262  frecsuclem  6269  xrrebnd  9542  fzpreddisj  9791  iseqf1olemqk  10207  gcdsupex  11542  gcdsupcl  11543  nndvdslegcd  11550  divgcdnn  11559  sqgcd  11613  coprm  11718  ctiunctlemudc  11845
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