Theorem nfe1 1545

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

Assertion

Ref	Expression
nfe1	⊢ Ⅎ𝑥∃𝑥𝜑

Proof of Theorem nfe1

Step	Hyp	Ref	Expression
1		hbe1 1544	. 2 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)
2	1	nfi 1511	1 ⊢ Ⅎ𝑥∃𝑥𝜑

Syntax hints:  Ⅎwnf 1509  ∃wex 1541

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 1498  ax-ie1 1542

This theorem depends on definitions:  df-bi 117  df-nf 1510

This theorem is referenced by:  nf3  1717  sb4or  1882  nfmo1  2092  euexex  2166  2moswapdc  2171  nfre1  2585  ceqsexg  2945  morex  3001  sbc6g  3067  intab  3978  nfopab1  4179  nfopab2  4180  copsexg  4360  copsex2t  4361  copsex2g  4362  eusv2nf  4577  onintonm  4639  mosubopt  4815  dmcoss  5027  imadif  5436  funimaexglem  5439  nfoprab1  6102  nfoprab2  6103  nfoprab3  6104  exmidfodomrlemr  7505  exmidfodomrlemrALT  7506  dfgrp3mlem  13811