Theorem nfeq1 2396

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 2386	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2394	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1398  Ⅎwnf 1509  Ⅎwnfc 2373

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 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-cleq 2227  df-clel 2230  df-nfc 2375

This theorem is referenced by:  euabsn  3766  invdisjrab  4108  fvmptt  5774  eusvobj2  6044  ovmpodv2  6195  ovi3  6199  dom2lem  7024  seq3f1olemstep  10900  seq3f1olemp  10901  fsumf1o  12101  isumss  12102  isummulc2  12137  fsum00  12173  isumshft  12201  fprodf1o  12299  prodssdc  12300