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Theorem pm5.42 570
Description: Theorem *5.42 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.42 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → (𝜓 → (𝜑𝜒))))

Proof of Theorem pm5.42
StepHypRef Expression
1 ibar 525 . . 3 (𝜑 → (𝜒 ↔ (𝜑𝜒)))
21imbi2d 330 . 2 (𝜑 → ((𝜓𝜒) ↔ (𝜓 → (𝜑𝜒))))
32pm5.74i 260 1 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → (𝜓 → (𝜑𝜒))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 384
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 386
This theorem is referenced by:  anc2l  577  imdistan  724
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