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

Theorem nfcri 2341
Description: Consequence of the not-free predicate. (Note that unlike nfcr 2339, this does not require  y and  A to be disjoint.) (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfcri.1  |-  F/_ x A
Assertion
Ref Expression
nfcri  |-  F/ x  y  e.  A
Distinct variable group:    x, y
Allowed substitution hints:    A( x, y)

Proof of Theorem nfcri
StepHypRef Expression
1 nfcri.1 . . 3  |-  F/_ x A
21nfcrii 2340 . 2  |-  ( y  e.  A  ->  A. x  y  e.  A )
32nfi 1484 1  |-  F/ x  y  e.  A
Colors of variables: wff set class
Syntax hints:   F/wnf 1482    e. wcel 2175   F/_wnfc 2334
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-io 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186
This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-cleq 2197  df-clel 2200  df-nfc 2336
This theorem is referenced by:  clelsb1f  2351  nfnfc  2354  nfeq  2355  nfel  2356  cleqf  2372  sbabel  2374  r2alf  2522  r2exf  2523  nfrabw  2686  cbvralfw  2727  cbvrexfw  2728  cbvralf  2729  cbvrexf  2730  cbvrab  2769  rmo3f  2969  nfccdeq  2995  sbcabel  3079  cbvcsbw  3096  cbvcsb  3097  cbvralcsf  3155  cbvrexcsf  3156  cbvreucsf  3157  cbvrabcsf  3158  dfss2f  3183  nfdif  3293  nfun  3328  nfin  3378  nfop  3834  nfiunxy  3952  nfiinxy  3953  nfiunya  3954  nfiinya  3955  cbviun  3963  cbviin  3964  iunxsngf  4004  cbvdisj  4030  nfdisjv  4032  disjiun  4038  nfmpt  4135  cbvmptf  4137  nffrfor  4394  onintrab2im  4565  tfis  4630  nfxp  4701  opeliunxp  4729  iunxpf  4825  elrnmpt1  4928  fvmptssdm  5663  nfmpo  6013  cbvmpox  6022  fmpox  6285  nffrec  6481  cc3  7379  nfsum1  11638  nfsum  11639  fsum2dlemstep  11716  fisumcom2  11720  nfcprod1  11836  nfcprod  11837  cbvprod  11840  fprod2dlemstep  11904  fprodcom2fi  11908  ctiunctlemudc  12779  ctiunctlemfo  12781
  Copyright terms: Public domain W3C validator