Theorem nfcsb 2878

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

Hypotheses

Ref	Expression
nfcsb.1	|- F/_xA
nfcsb.2	|- F/_xB

Assertion

Ref	Expression
nfcsb	|- F/_x [_A / y ]_B

Proof of Theorem nfcsb

Step	Hyp	Ref	Expression
1		nftru 1352	. . 3 |- F/y T.
2		nfcsb.1	. . . 4 |- F/_xA
3	2	a1i 9	. . 3 |- ( T. -> F/_xA)
4		nfcsb.2	. . . 4 |- F/_xB
5	4	a1i 9	. . 3 |- ( T. -> F/_xB)
6	1, 3, 5	nfcsbd 2877	. 2 |- ( T. -> F/_x [_A / y ]_B)
7	6	trud 1251	1 |- F/_x [_A / y ]_B

Syntax hints:   T. wtru 1243   F/_wnfc 2162   [_csb 2846

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-bndl 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-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-sbc 2759  df-csb 2847

This theorem is referenced by:  cbvralcsf  2902  cbvrexcsf  2903  cbvreucsf  2904  cbvrabcsf  2905  fmptcof  5274  mpt2mptsx  5765  dmmpt2ssx  5767  fmpt2x  5768  fmpt2co  5779  dfmpt2  5786