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Mirrors > Home > ILE Home > Th. List > jaob | GIF version |
Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. Alias of ax-io 699. (Contributed by NM, 30-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
jaob | ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-io 699 | 1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ↔ wb 104 ∨ wo 698 |
This theorem was proved from axioms: ax-io 699 |
This theorem is referenced by: olc 701 orc 702 pm3.44 705 pm4.77 789 pm5.53 792 unss 3255 ralunb 3262 intun 3810 intpr 3811 relop 4697 indstr 9415 algcvgblem 11766 sqrt2irr 11876 bj-inf2vnlem1 13339 |
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