Theorem nfeq1 2382

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

Hypothesis

Ref	Expression
nfeq1.1	|- F/_ x A

Assertion

Ref	Expression
nfeq1	|- F/ x A = B

Distinct variable group:   x, B

Allowed substitution hint:   A( x)

Proof of Theorem nfeq1

Step	Hyp	Ref	Expression
1		nfeq1.1	. 2 |- F/_ x A
2		nfcv 2372	. 2 |- F/_ x B
3	1, 2	nfeq 2380	1 |- F/ x A = B

Syntax hints:   = wceq 1395   F/wnf 1506   F/_wnfc 2359

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-cleq 2222  df-clel 2225  df-nfc 2361

This theorem is referenced by:  euabsn  3736  invdisjrab  4077  fvmptt  5728  eusvobj2  5993  ovmpodv2  6144  ovi3  6148  dom2lem  6931  seq3f1olemstep  10748  seq3f1olemp  10749  fsumf1o  11917  isumss  11918  isummulc2  11953  fsum00  11989  isumshft  12017  fprodf1o  12115  prodssdc  12116