Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-nfnfc Structured version   Unicode version

Theorem bj-nfnfc 31426
Description: Remove dependency on ax-ext 2401 (and df-cleq 2415) from nfnfc 2594. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-nfnfc.1  |-  F/_ x A
Assertion
Ref Expression
bj-nfnfc  |-  F/ x F/_ y A

Proof of Theorem bj-nfnfc
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2573 . 2  |-  ( F/_ y A  <->  A. z F/ y  z  e.  A )
2 bj-nfnfc.1 . . . . 5  |-  F/_ x A
32bj-nfcri 31425 . . . 4  |-  F/ x  z  e.  A
43nfnf 2006 . . 3  |-  F/ x F/ y  z  e.  A
54nfal 2004 . 2  |-  F/ x A. z F/ y  z  e.  A
61, 5nfxfr 1693 1  |-  F/ x F/_ y A
Colors of variables: wff setvar class
Syntax hints:   A.wal 1436   F/wnf 1664    e. wcel 1869   F/_wnfc 2571
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-ex 1661  df-nf 1665  df-sb 1788  df-clel 2418  df-nfc 2573
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator