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Theorem nfcri 2154
Description: Consequence of the not-free predicate. (Note that unlike nfcr 2152, 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 2153 . 2 (y Ax y A)
32nfi 1331 1 x y A
Colors of variables: wff set class
Syntax hints:  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-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-cleq 2015  df-clel 2018  df-nfc 2149
This theorem is referenced by:  nfnfc  2166  nfeq  2167  nfel  2168  cleqf  2183  sbabel  2185  r2alf  2319  r2exf  2320  nfrabxy  2468  cbvralf  2505  cbvrexf  2506  cbvrab  2533  nfccdeq  2739  sbcabel  2816  cbvcsb  2833  cbvralcsf  2885  cbvrexcsf  2886  cbvreucsf  2887  cbvrabcsf  2888  dfss2f  2913  nfdif  3042  nfun  3076  nfin  3120  nfop  3539  nfiunxy  3657  nfiinxy  3658  nfiunya  3659  nfiinya  3660  cbviun  3668  cbviin  3669  cbvdisj  3729  nfdisjv  3731  nfmpt  3823  tfis  4233  nfxp  4298  opeliunxp  4322  iunxpf  4411  elrnmpt1  4512  fvmptssdm  5180  nfmpt2  5496  cbvmpt2x  5505  fmpt2x  5749
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