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Theorem jaoa 627
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 ((φ θ) → ((ψ τ) → χ))

Proof of Theorem jaoa
StepHypRef Expression
1 jaao.1 . . 3 (φ → (ψχ))
21adantrd 264 . 2 (φ → ((ψ τ) → χ))
3 jaao.2 . . 3 (θ → (τχ))
43adantld 263 . 2 (θ → ((ψ τ) → χ))
52, 4jaoi 623 1 ((φ θ) → ((ψ τ) → χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wo 616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.79dc  802
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