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Mirrors > Home > ILE Home > Th. List > sylan9r | GIF version |
Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sylan9r.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
sylan9r.2 | ⊢ (𝜃 → (𝜒 → 𝜏)) |
Ref | Expression |
---|---|
sylan9r | ⊢ ((𝜃 ∧ 𝜑) → (𝜓 → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylan9r.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | sylan9r.2 | . . 3 ⊢ (𝜃 → (𝜒 → 𝜏)) | |
3 | 1, 2 | syl9r 72 | . 2 ⊢ (𝜃 → (𝜑 → (𝜓 → 𝜏))) |
4 | 3 | imp 122 | 1 ⊢ ((𝜃 ∧ 𝜑) → (𝜓 → 𝜏)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 |
This theorem is referenced by: spimt 1664 sbequi 1760 genpcdl 6709 genpcuu 6710 iccsupr 8989 climuni 10132 |
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