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Theorem imdi 376
Description: Distributive law for implication. Compare Theorem *5.41 of [WhiteheadRussell] p. 125. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
imdi ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) → (𝜑𝜒)))

Proof of Theorem imdi
StepHypRef Expression
1 ax-2 7 . 2 ((𝜑 → (𝜓𝜒)) → ((𝜑𝜓) → (𝜑𝜒)))
2 pm2.86 105 . 2 (((𝜑𝜓) → (𝜑𝜒)) → (𝜑 → (𝜓𝜒)))
31, 2impbii 197 1 ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) → (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194
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
This theorem is referenced by:  pm5.41  377  orimdi  887  bnj1174  30131  ifpim23g  36655
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