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Theorem imdistan 418
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)) ↔ ((φ ψ) → (φ χ)))

Proof of Theorem imdistan
StepHypRef Expression
1 pm5.42 303 . 2 ((φ → (ψχ)) ↔ (φ → (ψ → (φ χ))))
2 impexp 250 . 2 (((φ ψ) → (φ χ)) ↔ (φ → (ψ → (φ χ))))
31, 2bitr4i 176 1 ((φ → (ψχ)) ↔ ((φ ψ) → (φ χ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  imdistand  421  pm5.3  444  rmoim  2734  ss2rab  3010
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