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Mirrors > Home > ILE Home > Th. List > sylibr | GIF version |
Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting a consequent with a definition. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sylibr.1 | ⊢ (φ → ψ) |
sylibr.2 | ⊢ (χ ↔ ψ) |
Ref | Expression |
---|---|
sylibr | ⊢ (φ → χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylibr.1 | . 2 ⊢ (φ → ψ) | |
2 | sylibr.2 | . . 3 ⊢ (χ ↔ ψ) | |
3 | 2 | biimpri 124 | . 2 ⊢ (ψ → χ) |
4 | 1, 3 | syl 14 | 1 ⊢ (φ → χ) |
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