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Theorem pm5.3 743
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 impexp 460 . 2 (((𝜑𝜓) → 𝜒) ↔ (𝜑 → (𝜓𝜒)))
2 imdistan 720 . 2 ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) → (𝜑𝜒)))
31, 2bitri 262 1 (((𝜑𝜓) → 𝜒) ↔ ((𝜑𝜓) → (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  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:  clss2lem  36736
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