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Theorem intn3an3d 1377
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
intn3an3d  |-  ( ph  ->  -.  ( ch  /\  th 
/\  ps ) )

Proof of Theorem intn3an3d
StepHypRef Expression
1 intn3and.1 . 2  |-  ( ph  ->  -.  ps )
2 simp3 1008 . 2  |-  ( ( ch  /\  th  /\  ps )  ->  ps )
31, 2nsyl 125 1  |-  ( ph  ->  -.  ( ch  /\  th 
/\  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ w3a 983
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 189  df-an 373  df-3an 985
This theorem is referenced by:  en3lp  8125  winainflem  9120  spthispth  25295  2spotdisj  25781  gtnelioc  37462  icccncfext  37629  fourierdlem10  37843
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