Theorem nfeq1 2327

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 2317	. 2 |- F/_ x B
3	1, 2	nfeq 2325	1 |- F/ x A = B

Syntax hints:   = wceq 1353   F/wnf 1458   F/_wnfc 2304

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 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1459  df-sb 1761  df-cleq 2168  df-clel 2171  df-nfc 2306

This theorem is referenced by:  euabsn  3659  fvmptt  5599  eusvobj2  5851  ovmpodv2  5998  ovi3  6001  dom2lem  6762  seq3f1olemstep  10469  seq3f1olemp  10470  fsumf1o  11364  isumss  11365  isummulc2  11400  fsum00  11436  isumshft  11464  fprodf1o  11562  prodssdc  11563