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Theorem sbcom2v2 1862
 Description: Lemma for proving sbcom2 1863. It is the same as sbcom2v 1861 but removes the distinct variable constraint on and . (Contributed by Jim Kingdon, 19-Feb-2018.)
Assertion
Ref Expression
sbcom2v2
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem sbcom2v2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcom2v 1861 . . 3
2 sbcom2v 1861 . . . 4
32sbbii 1648 . . 3
41, 3bitri 173 . 2
5 ax-17 1419 . . . 4
65sbco2v 1821 . . 3
76sbbii 1648 . 2
8 ax-17 1419 . . 3
98sbco2v 1821 . 2
104, 7, 93bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wb 98  wsb 1645 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-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  sbcom2  1863
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