![]() |
Mathbox for Richard Penner |
< Previous
Next >
Nearby theorems |
|
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 2746 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 | ⊢ ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑 → 𝜓) → [𝑥 / 𝑦]𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege58bcor 39037 | . 2 ⊢ (∀𝑦(𝜑 → 𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓)) | |
2 | ax-frege8 38943 | . 2 ⊢ ((∀𝑦(𝜑 → 𝜓) → ([𝑥 / 𝑦]𝜑 → [𝑥 / 𝑦]𝜓)) → ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑 → 𝜓) → [𝑥 / 𝑦]𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑 → 𝜓) → [𝑥 / 𝑦]𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1656 [wsb 2069 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-10 2194 ax-12 2222 ax-13 2391 ax-frege8 38943 ax-frege58b 39035 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-ex 1881 df-nf 1885 df-sb 2070 |
This theorem is referenced by: frege63b 39042 frege64b 39043 |
Copyright terms: Public domain | W3C validator |