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  5726  eusvobj2  5987  ovmpodv2  6138  ovi3  6142  dom2lem  6923  seq3f1olemstep  10736  seq3f1olemp  10737  fsumf1o  11901  isumss  11902  isummulc2  11937  fsum00  11973  isumshft  12001  fprodf1o  12099  prodssdc  12100