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Theorem con4bii 311
Description: A contraposition inference. (Contributed by NM, 21-May-1994.)
Hypothesis
Ref Expression
con4bii.1 𝜑 ↔ ¬ 𝜓)
Assertion
Ref Expression
con4bii (𝜑𝜓)

Proof of Theorem con4bii
StepHypRef Expression
1 con4bii.1 . 2 𝜑 ↔ ¬ 𝜓)
2 notbi 309 . 2 ((𝜑𝜓) ↔ (¬ 𝜑 ↔ ¬ 𝜓))
31, 2mpbir 221 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196
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 197
This theorem is referenced by:  2false  365  2ralor  3104  gencbval  3247  snnzb  4245  raldifsnb  4316  uni0b  4454  opab0  4997  ceqsralv2  31582  tsna1  33922
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