Theorem nfeq1 2385

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 2375	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2383	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1398  Ⅎwnf 1509  Ⅎwnfc 2362

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-cleq 2224  df-clel 2227  df-nfc 2364

This theorem is referenced by:  euabsn  3745  invdisjrab  4087  fvmptt  5747  eusvobj2  6014  ovmpodv2  6165  ovi3  6169  dom2lem  6988  seq3f1olemstep  10822  seq3f1olemp  10823  fsumf1o  12014  isumss  12015  isummulc2  12050  fsum00  12086  isumshft  12114  fprodf1o  12212  prodssdc  12213