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Theorem jaoian 708
Description: Inference disjoining the antecedents of two implications. (Contributed by NM, 23-Oct-2005.)
Hypotheses
Ref Expression
jaoian.1 ((φ ψ) → χ)
jaoian.2 ((θ ψ) → χ)
Assertion
Ref Expression
jaoian (((φ θ) ψ) → χ)

Proof of Theorem jaoian
StepHypRef Expression
1 jaoian.1 . . . 4 ((φ ψ) → χ)
21ex 108 . . 3 (φ → (ψχ))
3 jaoian.2 . . . 4 ((θ ψ) → χ)
43ex 108 . . 3 (θ → (ψχ))
52, 4jaoi 635 . 2 ((φ θ) → (ψχ))
65imp 115 1 (((φ θ) ψ) → χ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wo 628
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 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  ordi  728  ccase  870
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