Theorem dveeq1 2044

Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.) Remove dependency on ax-11 1842. (Revised by Wolf Lammen, 8-Sep-2018.)

Assertion

Ref	Expression
dveeq1

Distinct variable group:   ,

Proof of Theorem dveeq1

Step	Hyp	Ref	Expression
1		nfeqf1 2043	. 2
2	1	nfrd 1875	1

Syntax hints:  -.wn 3  ->wi 4  A.wal 1393

This theorem is referenced by:  nfeqf  2045  axc11nlemOLD  2048  axc11n  2049  axc11nOLD  2050

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617