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Mirrors > Home > MPE Home > Th. List > nfequid | Structured version Visualization version 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 2024 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | 1 | nfth 1808 | 1 ⊢ Ⅎ𝑦 𝑥 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 |
This theorem depends on definitions: df-bi 210 df-ex 1787 df-nf 1791 |
This theorem is referenced by: (None) |
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