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Theorem imdistanda 422
Description: Distribution of implication with conjunction (deduction version with conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
imdistanda.1 ((φ ψ) → (χθ))
Assertion
Ref Expression
imdistanda (φ → ((ψ χ) → (ψ θ)))

Proof of Theorem imdistanda
StepHypRef Expression
1 imdistanda.1 . . 3 ((φ ψ) → (χθ))
21ex 108 . 2 (φ → (ψ → (χθ)))
32imdistand 421 1 (φ → ((ψ χ) → (ψ θ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
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:  fzind  8129  uzss  8269
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