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Mirrors > Home > MPE Home > Th. List > jaoi3 | Structured version Visualization version GIF version |
Description: Inference separating a disjunct of an antecedent. (Contributed by Alexander van der Vekens, 25-May-2018.) |
Ref | Expression |
---|---|
jaoi3.1 | ⊢ (𝜑 → 𝜓) |
jaoi3.2 | ⊢ ((¬ 𝜑 ∧ 𝜒) → 𝜓) |
Ref | Expression |
---|---|
jaoi3 | ⊢ ((𝜑 ∨ 𝜒) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jaoi3.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | jaoi3.2 | . . 3 ⊢ ((¬ 𝜑 ∧ 𝜒) → 𝜓) | |
3 | 1, 2 | jaoi 393 | . 2 ⊢ ((𝜑 ∨ (¬ 𝜑 ∧ 𝜒)) → 𝜓) |
4 | 3 | jaoi2 1002 | 1 ⊢ ((𝜑 ∨ 𝜒) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 ∧ wa 383 |
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 196 df-or 384 df-an 385 |
This theorem is referenced by: 2mpt20 6780 bropopvvv 7142 bropfvvvv 7144 ssnn0fi 12646 swrdnd 13284 2wlkonot3v 26402 2spthonot3v 26403 |
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