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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 709. (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 709 | 1 ⊢ (((𝜑 ∨ 𝜒) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (𝜒 → 𝜓))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 ↔ wb 105 ∨ wo 708 |
This theorem was proved from axioms: ax-io 709 |
This theorem is referenced by: olc 711 orc 712 pm3.44 715 pm4.77 799 pm5.53 802 unss 3309 ralunb 3316 intun 3875 intpr 3876 relop 4777 indstr 9592 algcvgblem 12048 sqrt2irr 12161 2sqlem6 14437 bj-inf2vnlem1 14692 |
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