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Theorem pm5.31 613
Description: Theorem *5.31 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.31 ((𝜒 ∧ (𝜑𝜓)) → (𝜑 → (𝜓𝜒)))

Proof of Theorem pm5.31
StepHypRef Expression
1 pm3.21 463 . . 3 (𝜒 → (𝜓 → (𝜓𝜒)))
21imim2d 57 . 2 (𝜒 → ((𝜑𝜓) → (𝜑 → (𝜓𝜒))))
32imp 444 1 ((𝜒 ∧ (𝜑𝜓)) → (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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  df-an 385
This theorem is referenced by:  bj-bary1lem1  33491
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