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Theorem pm5.18im 1292
Description: One direction of pm5.18dc 788, which holds for all propositions, not just decidable propositions. (Contributed by Jim Kingdon, 10-Mar-2018.)
Assertion
Ref Expression
pm5.18im ((𝜑𝜓) → ¬ (𝜑 ↔ ¬ 𝜓))

Proof of Theorem pm5.18im
StepHypRef Expression
1 pm5.19 632 . 2 ¬ (𝜓 ↔ ¬ 𝜓)
2 bibi1 233 . . 3 ((𝜑𝜓) → ((𝜑 ↔ ¬ 𝜓) ↔ (𝜓 ↔ ¬ 𝜓)))
32notbid 602 . 2 ((𝜑𝜓) → (¬ (𝜑 ↔ ¬ 𝜓) ↔ ¬ (𝜓 ↔ ¬ 𝜓)))
41, 3mpbiri 161 1 ((𝜑𝜓) → ¬ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  xornbi  1293
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