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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
StepHypRef Expression
1 csbhypf.1 . . . 4
21nfeq2 2636 . . 3
3 nfcsb1v 3450 . . . 4
4 csbhypf.2 . . . 4
53, 4nfeq 2630 . . 3
62, 5nfim 1920 . 2
7 eqeq1 2461 . . 3
8 csbeq1a 3443 . . . 4
98eqeq1d 2459 . . 3
107, 9imbi12d 320 . 2
11 csbhypf.3 . 2
126, 10, 11chvar 2013 1
 Colors of variables: wff setvar class 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
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