ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfrmo1 GIF version

Theorem nfrmo1 2499
Description: 𝑥 is not free in ∃*𝑥𝐴𝜑. (Contributed by NM, 16-Jun-2017.)
Assertion
Ref Expression
nfrmo1 𝑥∃*𝑥𝐴 𝜑

Proof of Theorem nfrmo1
StepHypRef Expression
1 df-rmo 2331 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
2 nfmo1 1928 . 2 𝑥∃*𝑥(𝑥𝐴𝜑)
31, 2nfxfr 1379 1 𝑥∃*𝑥𝐴 𝜑
Colors of variables: wff set class
Syntax hints:  wa 101  wnf 1365  wcel 1409  ∃*wmo 1917  ∃*wrmo 2326
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-eu 1919  df-mo 1920  df-rmo 2331
This theorem is referenced by:  nfdisj1  3785
  Copyright terms: Public domain W3C validator