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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege64b | Structured version Visualization version GIF version |
Description: Lemma for frege65b 40249. Proposition 64 of [Frege1879] p. 53. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege64b | ⊢ (([𝑥 / 𝑦]𝜑 → [𝑧 / 𝑦]𝜓) → (∀𝑦(𝜓 → 𝜒) → ([𝑥 / 𝑦]𝜑 → [𝑧 / 𝑦]𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege62b 40246 | . 2 ⊢ ([𝑧 / 𝑦]𝜓 → (∀𝑦(𝜓 → 𝜒) → [𝑧 / 𝑦]𝜒)) | |
2 | frege18 40157 | . 2 ⊢ (([𝑧 / 𝑦]𝜓 → (∀𝑦(𝜓 → 𝜒) → [𝑧 / 𝑦]𝜒)) → (([𝑥 / 𝑦]𝜑 → [𝑧 / 𝑦]𝜓) → (∀𝑦(𝜓 → 𝜒) → ([𝑥 / 𝑦]𝜑 → [𝑧 / 𝑦]𝜒)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (([𝑥 / 𝑦]𝜑 → [𝑧 / 𝑦]𝜓) → (∀𝑦(𝜓 → 𝜒) → ([𝑥 / 𝑦]𝜑 → [𝑧 / 𝑦]𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1531 [wsb 2065 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-10 2141 ax-12 2172 ax-frege1 40129 ax-frege2 40130 ax-frege8 40148 ax-frege58b 40240 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1777 df-nf 1781 df-sb 2066 |
This theorem is referenced by: frege65b 40249 |
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