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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege55lem2c | Structured version Visualization version GIF version |
Description: Core proof of Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege55lem2c | ⊢ (𝑥 = 𝐴 → [𝐴 / 𝑧]𝑧 = 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3467 | . . 3 ⊢ 𝑥 ∈ V | |
2 | 1 | frege54cor1c 43409 | . 2 ⊢ [𝑥 / 𝑧]𝑧 = 𝑥 |
3 | frege53c 43408 | . 2 ⊢ ([𝑥 / 𝑧]𝑧 = 𝑥 → (𝑥 = 𝐴 → [𝐴 / 𝑧]𝑧 = 𝑥)) | |
4 | 2, 3 | ax-mp 5 | 1 ⊢ (𝑥 = 𝐴 → [𝐴 / 𝑧]𝑧 = 𝑥) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1533 Vcvv 3463 [wsbc 3769 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 ax-frege8 43303 ax-frege52c 43382 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3465 df-sbc 3770 df-sn 4625 |
This theorem is referenced by: (None) |
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