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Theorem 3ori 1194
Description: Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)
Hypothesis
Ref Expression
3ori.1 (φ ψ χ)
Assertion
Ref Expression
3ori ((¬ φ ¬ ψ) → χ)

Proof of Theorem 3ori
StepHypRef Expression
1 ioran 668 . 2 (¬ (φ ψ) ↔ (¬ φ ¬ ψ))
2 3ori.1 . . . 4 (φ ψ χ)
3 df-3or 885 . . . 4 ((φ ψ χ) ↔ ((φ ψ) χ))
42, 3mpbi 133 . . 3 ((φ ψ) χ)
54ori 641 . 2 (¬ (φ ψ) → χ)
61, 5sylbir 125 1 ((¬ φ ¬ ψ) → χ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97   wo 628   w3o 883
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-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-3or 885
This theorem is referenced by: (None)
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