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Mirrors > Home > NFE Home > Th. List > sylan2br | GIF version |
Description: A syllogism inference. (Contributed by NM, 21-Apr-1994.) |
Ref | Expression |
---|---|
sylan2br.1 | ⊢ (χ ↔ φ) |
sylan2br.2 | ⊢ ((ψ ∧ χ) → θ) |
Ref | Expression |
---|---|
sylan2br | ⊢ ((ψ ∧ φ) → θ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylan2br.1 | . . 3 ⊢ (χ ↔ φ) | |
2 | 1 | biimpri 197 | . 2 ⊢ (φ → χ) |
3 | sylan2br.2 | . 2 ⊢ ((ψ ∧ χ) → θ) | |
4 | 2, 3 | sylan2 460 | 1 ⊢ ((ψ ∧ φ) → θ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: syl2anbr 466 imainss 5042 xpexr2 5110 funeu2 5132 imadif 5171 fnop 5186 fcnvres 5243 fnopovb 5557 fovrn 5604 fnovrn 5607 nchoicelem17 6305 |
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