Theorem nfe1 1520

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 1519	. 2 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑)
2	1	nfi 1486	1 ⊢ Ⅎ𝑥∃𝑥𝜑

Syntax hints:  Ⅎwnf 1484  ∃wex 1516

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 1473  ax-ie1 1517

This theorem depends on definitions:  df-bi 117  df-nf 1485

This theorem is referenced by:  nf3  1693  sb4or  1857  nfmo1  2067  euexex  2140  2moswapdc  2145  nfre1  2550  ceqsexg  2905  morex  2961  sbc6g  3027  intab  3920  nfopab1  4121  nfopab2  4122  copsexg  4296  copsex2t  4297  copsex2g  4298  eusv2nf  4511  onintonm  4573  mosubopt  4748  dmcoss  4957  imadif  5363  funimaexglem  5366  nfoprab1  6007  nfoprab2  6008  nfoprab3  6009  exmidfodomrlemr  7326  exmidfodomrlemrALT  7327  dfgrp3mlem  13505