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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 72 | . 2 ⊢ (𝜑 → (𝜃 → (𝜓 → 𝜏))) |
4 | 3 | com12 30 | 1 ⊢ (𝜃 → (𝜑 → (𝜓 → 𝜏))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: sylan9r 408 const 847 pm2.85dc 900 looinvdc 910 pclem6 1369 nfimd 1578 19.23t 1670 fununi 5264 dfimafn 5543 funimass3 5610 nnsub 8910 bj-con1st 13751 |
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