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

Theorem nfnfc1 2178
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 2164 . 2 (xAyx y A)
2 nfnf1 1433 . . 3 xx y A
32nfal 1465 . 2 xyx y A
41, 3nfxfr 1360 1 xxA
Colors of variables: wff set class
Syntax hints:  wal 1240  wnf 1346   wcel 1390  wnfc 2162
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 1333  ax-7 1334  ax-gen 1335  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-nfc 2164
This theorem is referenced by:  vtoclgft  2598  sbcralt  2828  sbcrext  2829  csbiebt  2880  nfopd  3557  nfimad  4620  nffvd  5130
  Copyright terms: Public domain W3C validator