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Theorem csbhypf 2885
 Description: Introduce an explicit substitution into an implicit substitution hypothesis. See sbhypf 2603 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 2189 . . 3
3 nfcsb1v 2882 . . . 4
4 csbhypf.2 . . . 4
53, 4nfeq 2185 . . 3
62, 5nfim 1464 . 2
7 eqeq1 2046 . . 3
8 csbeq1a 2860 . . . 4
98eqeq1d 2048 . . 3
107, 9imbi12d 223 . 2
11 csbhypf.3 . 2
126, 10, 11chvar 1640 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  wnfc 2165  csb 2852 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-sbc 2765  df-csb 2853 This theorem is referenced by:  tfisi  4310
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