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Mirrors > Home > NFE Home > Th. List > celarent | GIF version |
Description: "Celarent", one of the syllogisms of Aristotelian logic. No φ is ψ, and all χ is φ, therefore no χ is ψ. (In Aristotelian notation, EAE-1: MeP and SaM therefore SeP.) For example, given the "No reptiles have fur" and "All snakes are reptiles", therefore "No snakes have fur". Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 24-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.) |
Ref | Expression |
---|---|
celarent.maj | ⊢ ∀x(φ → ¬ ψ) |
celarent.min | ⊢ ∀x(χ → φ) |
Ref | Expression |
---|---|
celarent | ⊢ ∀x(χ → ¬ ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | celarent.maj | . 2 ⊢ ∀x(φ → ¬ ψ) | |
2 | celarent.min | . 2 ⊢ ∀x(χ → φ) | |
3 | 1, 2 | barbara 2301 | 1 ⊢ ∀x(χ → ¬ ψ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: (None) |
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