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Mirrors > Home > ILE Home > Th. List > equsb2 | GIF version |
Description: Substitution applied to an atomic wff. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
equsb2 | ⊢ [𝑦 / 𝑥]𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb2 1777 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥) | |
2 | equcomi 1714 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
3 | 1, 2 | mpg 1461 | 1 ⊢ [𝑦 / 𝑥]𝑦 = 𝑥 |
Colors of variables: wff set class |
Syntax hints: → wi 4 [wsb 1772 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 |
This theorem depends on definitions: df-bi 117 df-sb 1773 |
This theorem is referenced by: sbco 1978 |
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