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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege62b | Structured version Visualization version GIF version |
Description: A kind of Aristotelian inference. This judgement replaces the mode of inference barbara 2748 when the minor premise has a particular context. Proposition 62 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege62b | ⊢ ([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑 → 𝜓) → [𝑦 / 𝑥]𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege58bcor 40256 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓)) | |
2 | ax-frege8 40162 | . 2 ⊢ ((∀𝑥(𝜑 → 𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓)) → ([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑 → 𝜓) → [𝑦 / 𝑥]𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑 → 𝜓) → [𝑦 / 𝑥]𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1535 [wsb 2069 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-12 2177 ax-frege8 40162 ax-frege58b 40254 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1781 df-nf 1785 df-sb 2070 |
This theorem is referenced by: frege63b 40261 frege64b 40262 |
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