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Theorem jaoa 709
Description: Inference disjoining and conjoining the antecedents of two implications. (Contributed by Stefan Allan, 1-Nov-2008.)
Hypotheses
Ref Expression
jaao.1 (𝜑 → (𝜓𝜒))
jaao.2 (𝜃 → (𝜏𝜒))
Assertion
Ref Expression
jaoa ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))

Proof of Theorem jaoa
StepHypRef Expression
1 jaao.1 . . 3 (𝜑 → (𝜓𝜒))
21adantrd 277 . 2 (𝜑 → ((𝜓𝜏) → 𝜒))
3 jaao.2 . . 3 (𝜃 → (𝜏𝜒))
43adantld 276 . 2 (𝜃 → ((𝜓𝜏) → 𝜒))
52, 4jaoi 705 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm4.79dc  888
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