ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfnfc1 Structured version   GIF version

Theorem nfnfc1 2163
Description: x is bound in xA. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfnfc1 xxA

Proof of Theorem nfnfc1
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2149 . 2 (xAyx y A)
2 nfnf1 1418 . . 3 xx y A
32nfal 1450 . 2 xyx y A
41, 3nfxfr 1343 1 xxA
Colors of variables: wff set class
Syntax hints:  wal 1226  wnf 1329   wcel 1374  wnfc 2147
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-7 1317  ax-gen 1318  ax-4 1381  ax-ial 1409
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-nfc 2149
This theorem is referenced by:  vtoclgft  2581  sbcralt  2811  sbcrext  2812  csbiebt  2863  nfopd  3540  nfimad  4604  nffvd  5112
  Copyright terms: Public domain W3C validator