Theorem nfeq1 2360

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 2350	. 2 |- F/_ x B
3	1, 2	nfeq 2358	1 |- F/ x A = B

Syntax hints:   = wceq 1373   F/wnf 1484   F/_wnfc 2337

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-cleq 2200  df-clel 2203  df-nfc 2339

This theorem is referenced by:  euabsn  3713  invdisjrab  4053  fvmptt  5694  eusvobj2  5953  ovmpodv2  6102  ovi3  6106  dom2lem  6886  seq3f1olemstep  10696  seq3f1olemp  10697  fsumf1o  11816  isumss  11817  isummulc2  11852  fsum00  11888  isumshft  11916  fprodf1o  12014  prodssdc  12015