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Mirrors > Home > MPE Home > Th. List > equsb1 | Structured version Visualization version GIF version |
Description: Substitution applied to an atomic wff. (Contributed by NM, 10-May-1993.) |
Ref | Expression |
---|---|
equsb1 | ⊢ [𝑦 / 𝑥]𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb2 2482 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦) | |
2 | id 22 | . 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1896 | 1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 2067 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-12 2220 ax-13 2389 |
This theorem depends on definitions: df-bi 199 df-an 387 df-ex 1879 df-sb 2068 |
This theorem is referenced by: sbequ8ALT 2538 sbie 2539 pm13.183 3563 exss 5154 frege54cor1b 39023 sb5ALT 39564 sb5ALTVD 39962 |
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