Theorem nfeq1 2349

Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
nfeq1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfeq1	⊢ Ⅎ𝑥 𝐴 = 𝐵

Distinct variable group:   𝑥,𝐵

Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfeq1

Step	Hyp	Ref	Expression
1		nfeq1.1	. 2 ⊢ Ⅎ𝑥𝐴
2		nfcv 2339	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2347	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1364  Ⅎwnf 1474  Ⅎwnfc 2326

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-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-cleq 2189  df-clel 2192  df-nfc 2328

This theorem is referenced by:  euabsn  3692  fvmptt  5653  eusvobj2  5908  ovmpodv2  6056  ovi3  6060  dom2lem  6831  seq3f1olemstep  10606  seq3f1olemp  10607  fsumf1o  11555  isumss  11556  isummulc2  11591  fsum00  11627  isumshft  11655  fprodf1o  11753  prodssdc  11754