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Theorem 3jao 1243
 Description: Disjunction of 3 antecedents. (Contributed by NM, 8-Apr-1994.)
Assertion
Ref Expression
3jao (((φψ) (χψ) (θψ)) → ((φ χ θ) → ψ))

Proof of Theorem 3jao
StepHypRef Expression
1 df-3or 935 . 2 ((φ χ θ) ↔ ((φ χ) θ))
2 jao 498 . . . 4 ((φψ) → ((χψ) → ((φ χ) → ψ)))
3 jao 498 . . . 4 (((φ χ) → ψ) → ((θψ) → (((φ χ) θ) → ψ)))
42, 3syl6 29 . . 3 ((φψ) → ((χψ) → ((θψ) → (((φ χ) θ) → ψ))))
543imp 1145 . 2 (((φψ) (χψ) (θψ)) → (((φ χ) θ) → ψ))
61, 5syl5bi 208 1 (((φψ) (χψ) (θψ)) → ((φ χ θ) → ψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 357   ∨ 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:  3jaob  1244  3jaoi  1245  3jaod  1246
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