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Mirrors > Home > MPE Home > Th. List > equsb1 | Structured version Visualization version GIF version |
Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 2389. Use the weaker equsb1v 2111 if possible. (Contributed by NM, 10-May-1993.) (New usage is discouraged.) |
Ref | Expression |
---|---|
equsb1 | ⊢ [𝑦 / 𝑥]𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb2 2503 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦) | |
2 | id 22 | . 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1797 | 1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 2068 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-10 2144 ax-12 2176 ax-13 2389 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1780 df-nf 1784 df-sb 2069 |
This theorem is referenced by: sbequ8 2542 sbie 2543 pm13.183OLD 3663 frege54cor1b 40246 sb5ALT 40865 sb5ALTVD 41253 |
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