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Mirrors > Home > NFE Home > Th. List > syl6com | GIF version |
Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005.) |
Ref | Expression |
---|---|
syl6com.1 | ⊢ (φ → (ψ → χ)) |
syl6com.2 | ⊢ (χ → θ) |
Ref | Expression |
---|---|
syl6com | ⊢ (ψ → (φ → θ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6com.1 | . . 3 ⊢ (φ → (ψ → χ)) | |
2 | syl6com.2 | . . 3 ⊢ (χ → θ) | |
3 | 1, 2 | syl6 29 | . 2 ⊢ (φ → (ψ → θ)) |
4 | 3 | com12 27 | 1 ⊢ (ψ → (φ → θ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: 19.33b 1608 ax9 1949 ax16i 2046 ax16ALT2 2048 funcnvuni 5161 nchoicelem17 6305 |
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