Theorem nfre1 2507

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 2448	. 2 |- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
2		nfe1 1483	. 2 |- F/ x E. x ( x e. A /\ ph )
3	1, 2	nfxfr 1461	1 |- F/ x E. x e. A ph

Syntax hints:   /\ wa 103   F/wnf 1447   E.wex 1479   e. wcel 2135   E.wrex 2443

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1434  ax-gen 1436  ax-ie1 1480

This theorem depends on definitions:  df-bi 116  df-nf 1448  df-rex 2448

This theorem is referenced by:  r19.29an  2606  nfiu1  3890  fun11iun  5447  eusvobj2  5822  fodjuomnilemdc  7099  ismkvnex  7110  prarloclem3step  7428  prmuloc2  7499  ltexprlemm  7532  caucvgprprlemaddq  7640  caucvgsrlemgt1  7727  axpre-suploclemres  7833  supinfneg  9524  infsupneg  9525  lbzbi  9545  divalglemeunn  11843  divalglemeuneg  11845  bezoutlemmain  11916  bezout  11929  pw1nct  13717  isomninnlem  13743  trirec0  13757  ismkvnnlem  13765