Theorem nfeq1 2358

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 2348	. 2 |- F/_ x B
3	1, 2	nfeq 2356	1 |- F/ x A = B

Syntax hints:   = wceq 1373   F/wnf 1483   F/_wnfc 2335

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-cleq 2198  df-clel 2201  df-nfc 2337

This theorem is referenced by:  euabsn  3703  invdisjrab  4039  fvmptt  5673  eusvobj2  5932  ovmpodv2  6081  ovi3  6085  dom2lem  6865  seq3f1olemstep  10661  seq3f1olemp  10662  fsumf1o  11734  isumss  11735  isummulc2  11770  fsum00  11806  isumshft  11834  fprodf1o  11932  prodssdc  11933