Theorem nfcsb1d 3448

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

Hypothesis

Ref	Expression
nfcsb1d.1

Assertion

Ref	Expression
nfcsb1d

Proof of Theorem nfcsb1d

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-csb 3435	. 2
2		nfv 1707	. . 3
3		nfcsb1d.1	. . . 4
4	3	nfsbc1d 3345	. . 3
5	2, 4	nfabd 2641	. 2
6	1, 5	nfcxfrd 2618	1

Syntax hints:  ->wi 4  e.wcel 1818  {cab 2442  F/_wnfc 2605  [.wsbc 3327  [_csb 3434

This theorem is referenced by:  nfcsb1  3449

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  df-csb 3435