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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 498 | 1 ⊢ (𝜓 → ((𝜒 ∧ 𝜑) → 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 196 df-an 385 |
This theorem is referenced by: syl2ani 686 odi 7546 pssnn 8063 ltexprlem7 9743 ltaprlem 9745 sup2 10858 filufint 21534 pjnormssi 28411 poimirlem27 32606 poimirlem31 32610 pellex 36417 |
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