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Theorem jaoa 496
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 454 . 2 (φ → ((ψ τ) → χ))
3 jaao.2 . . 3 (θ → (τχ))
43adantld 453 . 2 (θ → ((ψ τ) → χ))
52, 4jaoi 368 1 ((φ θ) → ((ψ τ) → χ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wo 357   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
This theorem is referenced by:  pm4.79  566
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