Theorem nfre1 2593

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 2534	. 2 |- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
2		nfe1 1549	. 2 |- F/ x E. x ( x e. A /\ ph )
3	1, 2	nfxfr 1527	1 |- F/ x E. x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1513   E.wex 1545   e. wcel 2209   E.wrex 2529

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 1500  ax-gen 1502  ax-ie1 1546

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-rex 2534

This theorem is referenced by:  r19.29an  2693  nfiu1  4037  fun11iun  5655  eusvobj2  6061  fodjuomnilemdc  7474  ismkvnex  7485  prarloclem3step  7853  prmuloc2  7924  ltexprlemm  7957  caucvgprprlemaddq  8065  caucvgsrlemgt1  8152  axpre-suploclemres  8258  supinfneg  9974  infsupneg  9975  lbzbi  9995  divalglemeunn  12666  divalglemeuneg  12668  bezoutlemmain  12753  bezout  12766  lss1d  14692  pw1nct  16947  isomninnlem  16984  trirec0  16998  ismkvnnlem  17007