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Theorem nfcri 2169
Description: Consequence of the not-free predicate. (Note that unlike nfcr 2167, this does not require y and A to be disjoint.) (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfcri.1 xA
Assertion
Ref Expression
nfcri x y A
Distinct variable group:   x,y
Allowed substitution hints:   A(x,y)

Proof of Theorem nfcri
StepHypRef Expression
1 nfcri.1 . . 3 xA
21nfcrii 2168 . 2 (y Ax y A)
32nfi 1348 1 x y A
Colors of variables: wff set class
Syntax hints:  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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164
This theorem is referenced by:  nfnfc  2181  nfeq  2182  nfel  2183  cleqf  2198  sbabel  2200  r2alf  2335  r2exf  2336  nfrabxy  2484  cbvralf  2521  cbvrexf  2522  cbvrab  2549  nfccdeq  2756  sbcabel  2833  cbvcsb  2850  cbvralcsf  2902  cbvrexcsf  2903  cbvreucsf  2904  cbvrabcsf  2905  dfss2f  2930  nfdif  3059  nfun  3093  nfin  3137  nfop  3556  nfiunxy  3674  nfiinxy  3675  nfiunya  3676  nfiinya  3677  cbviun  3685  cbviin  3686  cbvdisj  3746  nfdisjv  3748  nfmpt  3840  tfis  4249  nfxp  4314  opeliunxp  4338  iunxpf  4427  elrnmpt1  4528  fvmptssdm  5198  nfmpt2  5515  cbvmpt2x  5524  fmpt2x  5768  nffrec  5921
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