Theorem nfe1 1519

Description: x is not free in E. x ph. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfe1	|- F/ x E. x ph

Proof of Theorem nfe1

Step	Hyp	Ref	Expression
1		hbe1 1518	. 2 |- ( E. x ph -> A. x E. x ph )
2	1	nfi 1485	1 |- F/ x E. x ph

Syntax hints:   F/wnf 1483   E.wex 1515

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-gen 1472  ax-ie1 1516

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

This theorem is referenced by:  nf3  1692  sb4or  1856  nfmo1  2066  euexex  2139  2moswapdc  2144  nfre1  2549  ceqsexg  2901  morex  2957  sbc6g  3023  intab  3914  nfopab1  4114  nfopab2  4115  copsexg  4289  copsex2t  4290  copsex2g  4291  eusv2nf  4504  onintonm  4566  mosubopt  4741  dmcoss  4949  imadif  5355  funimaexglem  5358  nfoprab1  5996  nfoprab2  5997  nfoprab3  5998  exmidfodomrlemr  7312  exmidfodomrlemrALT  7313  dfgrp3mlem  13463