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Mirrors > Home > ILE Home > Th. List > syl6 | GIF version |
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 30-Jul-2012.) |
Ref | Expression |
---|---|
syl6.1 | ⊢ (φ → (ψ → χ)) |
syl6.2 | ⊢ (χ → θ) |
Ref | Expression |
---|---|
syl6 | ⊢ (φ → (ψ → θ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | syl6.2 | . . 3 ⊢ (χ → θ) | |
3 | 2 | a1i 9 | . 2 ⊢ (ψ → (χ → θ)) |
4 | 1, 3 | sylcom 25 | 1 ⊢ (φ → (ψ → θ)) |
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