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Mirrors > Home > ILE Home > Th. List > mp3an12i | GIF version |
Description: mp3an 1268 with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016.) |
Ref | Expression |
---|---|
mp3an12i.1 | ⊢ 𝜑 |
mp3an12i.2 | ⊢ 𝜓 |
mp3an12i.3 | ⊢ (𝜒 → 𝜃) |
mp3an12i.4 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
mp3an12i | ⊢ (𝜒 → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mp3an12i.3 | . 2 ⊢ (𝜒 → 𝜃) | |
2 | mp3an12i.1 | . . 3 ⊢ 𝜑 | |
3 | mp3an12i.2 | . . 3 ⊢ 𝜓 | |
4 | mp3an12i.4 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) | |
5 | 2, 3, 4 | mp3an12 1258 | . 2 ⊢ (𝜃 → 𝜏) |
6 | 1, 5 | syl 14 | 1 ⊢ (𝜒 → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: oddp1d2 10290 bezoutlema 10388 bezoutlemb 10389 |
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