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Mirrors > Home > MPE Home > Th. List > sylan2i | Structured version Visualization version GIF version |
Description: A syllogism inference. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
sylan2i.1 | ⊢ (𝜑 → 𝜃) |
sylan2i.2 | ⊢ (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)) |
Ref | Expression |
---|---|
sylan2i | ⊢ (𝜓 → ((𝜒 ∧ 𝜑) → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylan2i.1 | . . 3 ⊢ (𝜑 → 𝜃) | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜓 → (𝜑 → 𝜃)) |
3 | sylan2i.2 | . 2 ⊢ (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)) | |
4 | 2, 3 | sylan2d 603 | 1 ⊢ (𝜓 → ((𝜒 ∧ 𝜑) → 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 |
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 206 df-an 395 |
This theorem is referenced by: syl2ani 605 odi 8604 pssnn 9197 pssnnOLD 9294 ltexprlem7 11071 ltaprlem 11073 sup2 12206 filufint 23842 pjnormssi 31996 poimirlem27 37125 poimirlem31 37129 sn-sup2 42027 pellex 42258 |
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