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  4113  nfopab2  4114  copsexg  4288  copsex2t  4289  copsex2g  4290  eusv2nf  4503  onintonm  4565  mosubopt  4740  dmcoss  4948  imadif  5354  funimaexglem  5357  nfoprab1  5994  nfoprab2  5995  nfoprab3  5996  exmidfodomrlemr  7310  exmidfodomrlemrALT  7311  dfgrp3mlem  13430