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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege53c | Structured version Visualization version GIF version |
Description: Proposition 53 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege53c | ⊢ ([𝐴 / 𝑥]𝜑 → (𝐴 = 𝐵 → [𝐵 / 𝑥]𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege52c 38499 | . 2 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑)) | |
2 | ax-frege8 38420 | . 2 ⊢ ((𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑)) → ([𝐴 / 𝑥]𝜑 → (𝐴 = 𝐵 → [𝐵 / 𝑥]𝜑))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝐴 / 𝑥]𝜑 → (𝐴 = 𝐵 → [𝐵 / 𝑥]𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1523 [wsbc 3468 |
This theorem was proved from axioms: ax-mp 5 ax-frege8 38420 ax-frege52c 38499 |
This theorem is referenced by: frege55lem2c 38528 frege55c 38529 frege56c 38530 frege92 38566 |
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