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Theorem pm5.3 576
Description: Theorem *5.3 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
pm5.3 (((𝜑𝜓) → 𝜒) ↔ ((𝜑𝜓) → (𝜑𝜒)))

Proof of Theorem pm5.3
StepHypRef Expression
1 simpl 486 . . 3 ((𝜑𝜓) → 𝜑)
21biantrurd 536 . 2 ((𝜑𝜓) → (𝜒 ↔ (𝜑𝜒)))
32pm5.74i 274 1 (((𝜑𝜓) → 𝜒) ↔ ((𝜑𝜓) → (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  cusgr3cyclex  32491  clss2lem  40298
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