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Mirrors > Home > ILE Home > Th. List > jao | GIF version |
Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.) |
Ref | Expression |
---|---|
jao | ⊢ ((φ → ψ) → ((χ → ψ) → ((φ ∨ χ) → ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.44 634 | . 2 ⊢ (((φ → ψ) ∧ (χ → ψ)) → ((φ ∨ χ) → ψ)) | |
2 | 1 | ex 108 | 1 ⊢ ((φ → ψ) → ((χ → ψ) → ((φ ∨ χ) → ψ))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ 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: 3jao 1195 suctr 4124 |
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