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Mirrors > Home > MPE Home > Th. List > sylanr2 | Structured version Visualization version GIF version |
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.) |
Ref | Expression |
---|---|
sylanr2.1 | ⊢ (𝜑 → 𝜃) |
sylanr2.2 | ⊢ ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏) |
Ref | Expression |
---|---|
sylanr2 | ⊢ ((𝜓 ∧ (𝜒 ∧ 𝜑)) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylanr2.1 | . . 3 ⊢ (𝜑 → 𝜃) | |
2 | 1 | anim2i 616 | . 2 ⊢ ((𝜒 ∧ 𝜑) → (𝜒 ∧ 𝜃)) |
3 | sylanr2.2 | . 2 ⊢ ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏) | |
4 | 2, 3 | sylan2 592 | 1 ⊢ ((𝜓 ∧ (𝜒 ∧ 𝜑)) → 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 208 df-an 397 |
This theorem is referenced by: adantrrl 720 adantrrr 721 isfin7-2 9806 mulsub 11071 fzsubel 12931 expsub 13465 ramlb 16343 0ram 16344 ressmplvsca 20168 tgcl 21505 fgss2 22410 nmoid 23278 numclwwlkqhash 28081 chirredlem4 30097 pibt2 34580 lindsadd 34766 poimirlem28 34801 pridlc3 35232 stoweidlem34 42196 |
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