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Mirrors > Home > ILE Home > Th. List > syl9r | GIF version |
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
syl9r.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
syl9r.2 | ⊢ (𝜃 → (𝜒 → 𝜏)) |
Ref | Expression |
---|---|
syl9r | ⊢ (𝜃 → (𝜑 → (𝜓 → 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl9r.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | syl9r.2 | . . 3 ⊢ (𝜃 → (𝜒 → 𝜏)) | |
3 | 1, 2 | syl9 66 | . 2 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜏))) |
4 | 3 | com12 27 | 1 ⊢ (𝜃 → (𝜑 → (𝜓 → 𝜏))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: sylan9r 390 pm2.85dc 811 looinvdc 821 pclem6 1265 nfimd 1477 19.23t 1567 fununi 4967 dfimafn 5222 funimass3 5283 nnsub 7952 |
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