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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege57b | Structured version Visualization version GIF version |
Description: Analogue of frege57aid 38166. Proposition 57 of [Frege1879] p. 51. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege57b | ⊢ (𝑥 = 𝑦 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege52b 38183 | . 2 ⊢ (𝑦 = 𝑥 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑)) | |
2 | frege56b 38192 | . 2 ⊢ ((𝑦 = 𝑥 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑)) → (𝑥 = 𝑦 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝑥 = 𝑦 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 1880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-12 2047 ax-13 2246 ax-ext 2602 ax-frege1 38084 ax-frege2 38085 ax-frege8 38103 ax-frege52c 38182 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-sbc 3436 |
This theorem is referenced by: (None) |
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