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Mirrors > Home > NFE 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 1676 | . 2 ⊢ x = x | |
2 | 1 | nfth 1553 | 1 ⊢ Ⅎy x = x |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1544 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 |
This theorem is referenced by: (None) |
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