Theorem nfequid 1700

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.)

Assertion

Ref	Expression
nfequid	⊢ Ⅎ𝑦 𝑥 = 𝑥

Proof of Theorem nfequid

Step	Hyp	Ref	Expression
1		equid 1699	. 2 ⊢ 𝑥 = 𝑥
2	1	nfth 1462	1 ⊢ Ⅎ𝑦 𝑥 = 𝑥

Syntax hints:  Ⅎwnf 1458

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1447  ax-ie2 1492  ax-8 1502  ax-17 1524  ax-i9 1528

This theorem depends on definitions:  df-bi 117  df-nf 1459

This theorem is referenced by: (None)