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Theorem imnani 624
Description: Express implication in terms of conjunction. (Contributed by Mario Carneiro, 28-Sep-2015.)
Hypothesis
Ref Expression
imnani.1 ¬ (φ ψ)
Assertion
Ref Expression
imnani (φ → ¬ ψ)

Proof of Theorem imnani
StepHypRef Expression
1 imnani.1 . 2 ¬ (φ ψ)
2 imnan 623 . 2 ((φ → ¬ ψ) ↔ ¬ (φ ψ))
31, 2mpbir 134 1 (φ → ¬ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  eueq3dc  2709  dtruex  4237  nntri2  6012  nndcel  6016
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