Theorem nfre1 2549

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 2490	. 2 |- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
2		nfe1 1519	. 2 |- F/ x E. x ( x e. A /\ ph )
3	1, 2	nfxfr 1497	1 |- F/ x E. x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1483   E.wex 1515   e. wcel 2176   E.wrex 2485

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 1470  ax-gen 1472  ax-ie1 1516

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-rex 2490

This theorem is referenced by:  r19.29an  2648  nfiu1  3957  fun11iun  5543  eusvobj2  5930  fodjuomnilemdc  7246  ismkvnex  7257  prarloclem3step  7609  prmuloc2  7680  ltexprlemm  7713  caucvgprprlemaddq  7821  caucvgsrlemgt1  7908  axpre-suploclemres  8014  supinfneg  9716  infsupneg  9717  lbzbi  9737  divalglemeunn  12232  divalglemeuneg  12234  bezoutlemmain  12319  bezout  12332  lss1d  14145  pw1nct  15944  isomninnlem  15973  trirec0  15987  ismkvnnlem  15995