Theorem nfcsb 2965

Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)

Hypotheses

Ref	Expression
nfcsb.1	|- F/_ x A
nfcsb.2	|- F/_ x B

Assertion

Ref	Expression
nfcsb	|- F/_ x [_ A / y ]_ B

Proof of Theorem nfcsb

Step	Hyp	Ref	Expression
1		nftru 1400	. . 3 |- F/ y T.
2		nfcsb.1	. . . 4 |- F/_ x A
3	2	a1i 9	. . 3 |- ( T. -> F/_ x A )
4		nfcsb.2	. . . 4 |- F/_ x B
5	4	a1i 9	. . 3 |- ( T. -> F/_ x B )
6	1, 3, 5	nfcsbd 2964	. 2 |- ( T. -> F/_ x [_ A / y ]_ B )
7	6	mptru 1298	1 |- F/_ x [_ A / y ]_ B

Syntax hints:   T. wtru 1290   F/_wnfc 2215   [_csb 2933

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-sbc 2841  df-csb 2934

This theorem is referenced by:  cbvralcsf  2990  cbvrexcsf  2991  cbvreucsf  2992  cbvrabcsf  2993  fmptcof  5465  mpt2mptsx  5967  dmmpt2ssx  5969  fmpt2x  5970  fmpt2co  5981  dfmpt2  5988  f1od2  6000  nfsum  10742  fsum2dlemstep  10824  fisumcom2  10828