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Mirrors > Home > ILE Home > Th. List > nfequid | GIF version |
Description: Bound-variable hypothesis builder for 𝑥 = 𝑥. This theorem tells us that any variable, including 𝑥, is effectively not free in 𝑥 = 𝑥, even though 𝑥 is technically free according to the traditional definition of free variable. (Contributed by NM, 13-Jan-2011.) (Revised by NM, 21-Aug-2017.) |
Ref | Expression |
---|---|
nfequid | ⊢ Ⅎ𝑦 𝑥 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1629 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | 1 | nfth 1393 | 1 ⊢ Ⅎ𝑦 𝑥 = 𝑥 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1389 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-gen 1378 ax-ie2 1423 ax-8 1435 ax-17 1459 ax-i9 1463 |
This theorem depends on definitions: df-bi 115 df-nf 1390 |
This theorem is referenced by: (None) |
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