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Theorem imdistan 426
Description: Distribution of implication with conjunction. (Contributed by NM, 31-May-1999.) (Proof shortened by Wolf Lammen, 6-Dec-2012.)
Assertion
Ref Expression
imdistan ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) → (𝜑𝜒)))

Proof of Theorem imdistan
StepHypRef Expression
1 pm5.42 307 . 2 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → (𝜓 → (𝜑𝜒))))
2 impexp 254 . 2 (((𝜑𝜓) → (𝜑𝜒)) ↔ (𝜑 → (𝜓 → (𝜑𝜒))))
31, 2bitr4i 180 1 ((𝜑 → (𝜓𝜒)) ↔ ((𝜑𝜓) → (𝜑𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  imdistand  429  pm5.3  452  rmoim  2763  ss2rab  3044
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