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Theorem imnani 663
Description: Express implication in terms of conjunction. (Contributed by Mario Carneiro, 28-Sep-2015.)
Hypothesis
Ref Expression
imnani.1 ¬ (𝜑𝜓)
Assertion
Ref Expression
imnani (𝜑 → ¬ 𝜓)

Proof of Theorem imnani
StepHypRef Expression
1 imnani.1 . 2 ¬ (𝜑𝜓)
2 imnan 662 . 2 ((𝜑 → ¬ 𝜓) ↔ ¬ (𝜑𝜓))
31, 2mpbir 145 1 (𝜑 → ¬ 𝜓)
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 586  ax-in2 587
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mptnan  1384  eueq3dc  2829  dtruex  4442  nntri2  6356  nndcel  6362
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