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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 857 | . 2 ⊢ ((𝜑 ∨ (¬ 𝜑 ∧ 𝜒)) → 𝜓) |
4 | 3 | jaoi2 1059 | 1 ⊢ ((𝜑 ∨ 𝜒) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 395 ∨ wo 847 |
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 207 df-an 396 df-or 848 |
This theorem is referenced by: 2mpo0 7682 bropopvvv 8114 bropfvvvv 8116 ssnn0fi 14023 swrdnd 14689 swrdnnn0nd 14691 swrdnd0 14692 pfxnd0 14723 line2ylem 48601 line2xlem 48603 itsclc0xyqsol 48618 |
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