Theorem nfre1 2365

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 2312	. 2 |- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
2		nfe1 1385	. 2 |- F/ x E. x ( x e. A /\ ph )
3	1, 2	nfxfr 1363	1 |- F/ x E. x e. A ph

Syntax hints:   /\ wa 97   F/wnf 1349   E.wex 1381   e. wcel 1393   E.wrex 2307

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-rex 2312

This theorem is referenced by:  nfiu1  3687  fun11iun  5147  eusvobj2  5498  prarloclem3step  6594  prmuloc2  6665  ltexprlemm  6698  caucvgprprlemaddq  6806  caucvgsrlemgt1  6879  lbzbi  8551