Theorem nfeq1 2357

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 2347	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfeq 2355	1 ⊢ Ⅎ𝑥 𝐴 = 𝐵

Syntax hints:   = wceq 1372  Ⅎwnf 1482  Ⅎwnfc 2334

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-cleq 2197  df-clel 2200  df-nfc 2336

This theorem is referenced by:  euabsn  3702  fvmptt  5665  eusvobj2  5920  ovmpodv2  6069  ovi3  6073  dom2lem  6849  seq3f1olemstep  10640  seq3f1olemp  10641  fsumf1o  11620  isumss  11621  isummulc2  11656  fsum00  11692  isumshft  11720  fprodf1o  11818  prodssdc  11819