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Mirrors > Home > MPE Home > Th. List > equsb1v | Structured version Visualization version GIF version |
Description: Version of equsb1 2500 with a disjoint variable condition, which does not require ax-13 2391. (Contributed by BJ, 11-Sep-2019.) |
Ref | Expression |
---|---|
equsb1v | ⊢ [𝑦 / 𝑥]𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb2v 2302 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦) | |
2 | id 22 | . 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1898 | 1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 2069 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-12 2222 |
This theorem depends on definitions: df-bi 199 df-an 387 df-ex 1881 df-sb 2070 |
This theorem is referenced by: sbiev 2345 |
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