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Theorem jaao 495
Description: Inference conjoining and disjoining the antecedents of two implications. (Contributed by NM, 30-Sep-1999.)
Hypotheses
Ref Expression
jaao.1 (φ → (ψχ))
jaao.2 (θ → (τχ))
Assertion
Ref Expression
jaao ((φ θ) → ((ψ τ) → χ))

Proof of Theorem jaao
StepHypRef Expression
1 jaao.1 . . 3 (φ → (ψχ))
21adantr 451 . 2 ((φ θ) → (ψχ))
3 jaao.2 . . 3 (θ → (τχ))
43adantl 452 . 2 ((φ θ) → (τχ))
52, 4jaod 369 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:  pm3.44  497  pm3.48  806  prlem1  928  funun  5146
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