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Theorem pm3.37 600
Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 23-Oct-2012.)
Assertion
Ref Expression
pm3.37 (((𝜑𝜓) → 𝜒) → ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓))

Proof of Theorem pm3.37
StepHypRef Expression
1 pm4.14 599 . 2 (((𝜑𝜓) → 𝜒) ↔ ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓))
21biimpi 204 1 (((𝜑𝜓) → 𝜒) → ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by: (None)
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