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Theorem imnani 680
Description: Express implication in terms of conjunction. (Contributed by Mario Carneiro, 28-Sep-2015.)
Hypothesis
Ref Expression
imnani.1  |-  -.  ( ph  /\  ps )
Assertion
Ref Expression
imnani  |-  ( ph  ->  -.  ps )

Proof of Theorem imnani
StepHypRef Expression
1 imnani.1 . 2  |-  -.  ( ph  /\  ps )
2 imnan 679 . 2  |-  ( (
ph  ->  -.  ps )  <->  -.  ( ph  /\  ps ) )
31, 2mpbir 145 1  |-  ( ph  ->  -.  ps )
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-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mptnan  1401  eueq3dc  2853  dtruex  4469  nntri2  6383  nndcel  6389
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