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Theorem pm4.15 827
Description: Theorem *4.15 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 18-Nov-2012.)
Assertion
Ref Expression
pm4.15 (((𝜑𝜓) → ¬ 𝜒) ↔ ((𝜓𝜒) → ¬ 𝜑))

Proof of Theorem pm4.15
StepHypRef Expression
1 con2b 628 . 2 (((𝜓𝜒) → ¬ 𝜑) ↔ (𝜑 → ¬ (𝜓𝜒)))
2 nan 661 . 2 ((𝜑 → ¬ (𝜓𝜒)) ↔ ((𝜑𝜓) → ¬ 𝜒))
31, 2bitr2i 183 1 (((𝜑𝜓) → ¬ 𝜒) ↔ ((𝜓𝜒) → ¬ 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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