Theorem csbhypf 3453

Description: Introduce an explicit substitution into an implicit substitution hypothesis. See sbhypf 3156 for class substitution version. (Contributed by NM, 19-Dec-2008.)

Hypotheses

Ref	Expression
csbhypf.1
csbhypf.2
csbhypf.3

Assertion

Ref	Expression
csbhypf

Distinct variable group:   ,

Proof of Theorem csbhypf

Step	Hyp	Ref	Expression
1		csbhypf.1	. . . 4
2	1	nfeq2 2636	. . 3
3		nfcsb1v 3450	. . . 4
4		csbhypf.2	. . . 4
5	3, 4	nfeq 2630	. . 3
6	2, 5	nfim 1920	. 2
7		eqeq1 2461	. . 3
8		csbeq1a 3443	. . . 4
9	8	eqeq1d 2459	. . 3
10	7, 9	imbi12d 320	. 2
11		csbhypf.3	. 2
12	6, 10, 11	chvar 2013	1

Syntax hints:  ->wi 4  =wceq 1395  F/_wnfc 2605  [_csb 3434

This theorem is referenced by:  disji2  4439  disjprg  4448  disjxun  4450  tfisi  6693  coe1fzgsumdlem  18343  evl1gsumdlem  18392  iundisj2  21959  disji2f  27438  disjif2  27442  iundisj2f  27449  iundisj2fi  27602

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