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Theorem intn3an2d 25040
Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Hypothesis
Ref Expression
intn3and.1  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
intn3an2d  |-  ( ph  ->  -.  ( ch  /\  ps  /\  th ) )

Proof of Theorem intn3an2d
StepHypRef Expression
1 intn3and.1 . 2  |-  ( ph  ->  -.  ps )
2 simp2 956 . 2  |-  ( ( ch  /\  ps  /\  th )  ->  ps )
31, 2nsyl 113 1  |-  ( ph  ->  -.  ( ch  /\  ps  /\  th ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ w3a 934
This theorem is referenced by:  iintlem1  25713
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  df-3an 936
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