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Mirrors > Home > MPE Home > Th. List > sylani | Structured version Visualization version GIF version |
Description: A syllogism inference. (Contributed by NM, 2-May-1996.) |
Ref | Expression |
---|---|
sylani.1 | ⊢ (𝜑 → 𝜒) |
sylani.2 | ⊢ (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)) |
Ref | Expression |
---|---|
sylani | ⊢ (𝜓 → ((𝜑 ∧ 𝜃) → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylani.1 | . . 3 ⊢ (𝜑 → 𝜒) | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) |
3 | sylani.2 | . 2 ⊢ (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)) | |
4 | 2, 3 | syland 603 | 1 ⊢ (𝜓 → ((𝜑 ∧ 𝜃) → 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
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 397 |
This theorem is referenced by: syl2ani 607 inf3lem2 9387 zorn2lem5 10256 uzwo 12651 supxrun 13050 lcmdvds 16313 cramer0 21839 csmdsymi 30696 matunitlindflem2 35774 pmapjoin 37866 |
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