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Theorem imdistanda 430
Description: Distribution of implication with conjunction (deduction version with conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
imdistanda.1 ((𝜑𝜓) → (𝜒𝜃))
Assertion
Ref Expression
imdistanda (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))

Proof of Theorem imdistanda
StepHypRef Expression
1 imdistanda.1 . . 3 ((𝜑𝜓) → (𝜒𝜃))
21ex 112 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32imdistand 429 1 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
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:  fzind  8412  uzss  8589  qbtwnzlemshrink  9206  rebtwn2zlemshrink  9210  cau3lem  9941
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