Theorem nfre1 2573

Description: x is not free in E. x e. A ph. (Contributed by NM, 19-Mar-1997.) (Revised by Mario Carneiro, 7-Oct-2016.)

Assertion

Ref	Expression
nfre1	|- F/ x E. x e. A ph

Proof of Theorem nfre1

Step	Hyp	Ref	Expression
1		df-rex 2514	. 2 |- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
2		nfe1 1542	. 2 |- F/ x E. x ( x e. A /\ ph )
3	1, 2	nfxfr 1520	1 |- F/ x E. x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1506   E.wex 1538   e. wcel 2200   E.wrex 2509

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-5 1493  ax-gen 1495  ax-ie1 1539

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-rex 2514

This theorem is referenced by:  r19.29an  2673  nfiu1  3995  fun11iun  5595  eusvobj2  5993  fodjuomnilemdc  7322  ismkvnex  7333  prarloclem3step  7694  prmuloc2  7765  ltexprlemm  7798  caucvgprprlemaddq  7906  caucvgsrlemgt1  7993  axpre-suploclemres  8099  supinfneg  9802  infsupneg  9803  lbzbi  9823  divalglemeunn  12448  divalglemeuneg  12450  bezoutlemmain  12535  bezout  12548  lss1d  14363  pw1nct  16456  isomninnlem  16486  trirec0  16500  ismkvnnlem  16508