Theorem nfre1 2520

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 2461	. 2 |- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
2		nfe1 1496	. 2 |- F/ x E. x ( x e. A /\ ph )
3	1, 2	nfxfr 1474	1 |- F/ x E. x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1460   E.wex 1492   e. wcel 2148   E.wrex 2456

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 1447  ax-gen 1449  ax-ie1 1493

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-rex 2461

This theorem is referenced by:  r19.29an  2619  nfiu1  3916  fun11iun  5480  eusvobj2  5857  fodjuomnilemdc  7138  ismkvnex  7149  prarloclem3step  7491  prmuloc2  7562  ltexprlemm  7595  caucvgprprlemaddq  7703  caucvgsrlemgt1  7790  axpre-suploclemres  7896  supinfneg  9590  infsupneg  9591  lbzbi  9611  divalglemeunn  11917  divalglemeuneg  11919  bezoutlemmain  11990  bezout  12003  pw1nct  14603  isomninnlem  14629  trirec0  14643  ismkvnnlem  14651