![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 2363. Use the weaker equsb1v 2095 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 2470 | . 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦) | |
2 | id 22 | . 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦) | |
3 | 1, 2 | mpg 1791 | 1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 2059 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-10 2129 ax-12 2163 ax-13 2363 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-ex 1774 df-nf 1778 df-sb 2060 |
This theorem is referenced by: sbequ8 2492 sbie 2493 frege54cor1b 43195 sb5ALT 43836 sb5ALTVD 44224 |
Copyright terms: Public domain | W3C validator |