Theorem nfsbc 3349

Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 7-Sep-2014.) (Revised by Mario Carneiro, 12-Oct-2016.)

Hypotheses

Ref	Expression
nfsbc.1
nfsbc.2

Assertion

Ref	Expression
nfsbc

Proof of Theorem nfsbc

Step	Hyp	Ref	Expression
1		nftru 1626	. . 3
2		nfsbc.1	. . . 4
3	2	a1i 11	. . 3
4		nfsbc.2	. . . 4
5	4	a1i 11	. . 3
6	1, 3, 5	nfsbcd 3348	. 2
7	6	trud 1404	1

Syntax hints:  wtru 1396  F/wnf 1616  F/_wnfc 2605  [.wsbc 3327

This theorem is referenced by:  cbvralcsf  3466  opelopabgf  4772  opelopabf  4777  ralrnmpt  6040  elovmpt2rab  6521  elovmpt2rab1  6522  ovmpt3rabdm  6535  elovmpt3rab1  6536  dfopab2  6854  dfoprab3s  6855  mpt2xopoveq  6966  elmptrab  20328  indexa  30224  sdclem1  30236  sbcalf  30517  sbcexf  30518  sbccomieg  30726  rexrabdioph  30727  bnj1445  34100  bnj1446  34101  bnj1467  34110

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-sbc 3328