Theorem nfeq1 2359

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 2349	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2357	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1373  Ⅎwnf 1484  Ⅎwnfc 2336

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-cleq 2199  df-clel 2202  df-nfc 2338

This theorem is referenced by:  euabsn  3708  invdisjrab  4045  fvmptt  5684  eusvobj2  5943  ovmpodv2  6092  ovi3  6096  dom2lem  6876  seq3f1olemstep  10681  seq3f1olemp  10682  fsumf1o  11776  isumss  11777  isummulc2  11812  fsum00  11848  isumshft  11876  fprodf1o  11974  prodssdc  11975