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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege62a | Structured version Visualization version GIF version |
Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara 2664 when the minor premise has a particular context. Proposition 62 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege62a | ⊢ (if-(𝜑, 𝜓, 𝜃) → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege58acor 41444 | . 2 ⊢ (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏))) | |
2 | ax-frege8 41377 | . 2 ⊢ ((((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏))) → (if-(𝜑, 𝜓, 𝜃) → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (if-(𝜑, 𝜓, 𝜃) → (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, 𝜒, 𝜏))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 if-wif 1060 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-frege8 41377 ax-frege58a 41443 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-ifp 1061 |
This theorem is referenced by: frege63a 41449 frege64a 41450 |
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