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Theorem 3jaoi 1245
Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)
Hypotheses
Ref Expression
3jaoi.1 (φψ)
3jaoi.2 (χψ)
3jaoi.3 (θψ)
Assertion
Ref Expression
3jaoi ((φ χ θ) → ψ)

Proof of Theorem 3jaoi
StepHypRef Expression
1 3jaoi.1 . . 3 (φψ)
2 3jaoi.2 . . 3 (χψ)
3 3jaoi.3 . . 3 (θψ)
41, 2, 33pm3.2i 1130 . 2 ((φψ) (χψ) (θψ))
5 3jao 1243 . 2 (((φψ) (χψ) (θψ)) → ((φ χ θ) → ψ))
64, 5ax-mp 5 1 ((φ χ θ) → ψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   w3o 933   w3a 934
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  df-3or 935  df-3an 936
This theorem is referenced by:  3jaoian  1247
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