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Theorem csbhypf 3279
 Description: Introduce an explicit substitution into an implicit substitution hypothesis. See sbhypf 2994 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:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem csbhypf
StepHypRef Expression
1 csbhypf.1 . . . 4
21nfeq2 2583 . . 3
3 nfcsb1v 3276 . . . 4
4 csbhypf.2 . . . 4
53, 4nfeq 2579 . . 3
62, 5nfim 1832 . 2
7 eqeq1 2442 . . 3
8 csbeq1a 3252 . . . 4
98eqeq1d 2444 . . 3
107, 9imbi12d 312 . 2
11 csbhypf.3 . 2
126, 10, 11chvar 1968 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652  wnfc 2559  csb 3244 This theorem is referenced by:  disji2  4192  disjprg  4201  disjxun  4203  tfisi  4831  iundisj2  19436  disji2f  24012  disjif2  24016  iundisj2f  24023  iundisj2fi  24146 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-sbc 3155  df-csb 3245
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