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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege57b | Structured version Visualization version GIF version |
Description: Analogue of frege57aid 40209. 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 40226 | . 2 ⊢ (𝑦 = 𝑥 → ([𝑦 / 𝑧]𝜑 → [𝑥 / 𝑧]𝜑)) | |
2 | frege56b 40235 | . 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 2063 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-12 2170 ax-13 2384 ax-ext 2791 ax-frege1 40127 ax-frege2 40128 ax-frege8 40146 ax-frege52c 40225 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1775 df-nf 1779 df-sb 2064 df-clab 2798 df-cleq 2812 df-clel 2891 df-sbc 3771 |
This theorem is referenced by: (None) |
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