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Theorem sbcom2v 1903
 Description: Lemma for proving sbcom2 1905. It is the same as sbcom2 1905 but with additional distinct variable constraints on and , and on and . (Contributed by Jim Kingdon, 19-Feb-2018.)
Assertion
Ref Expression
sbcom2v
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,,)

Proof of Theorem sbcom2v
StepHypRef Expression
1 alcom 1408 . . 3
2 bi2.04 246 . . . . . 6
32albii 1400 . . . . 5
4 19.21v 1795 . . . . 5
53, 4bitri 182 . . . 4
65albii 1400 . . 3
7 19.21v 1795 . . . 4
87albii 1400 . . 3
91, 6, 83bitr3i 208 . 2
10 sb6 1808 . . 3
11 sb6 1808 . . . . 5
1211imbi2i 224 . . . 4
1312albii 1400 . . 3
1410, 13bitri 182 . 2
15 sb6 1808 . . 3
16 sb6 1808 . . . . 5
1716imbi2i 224 . . . 4
1817albii 1400 . . 3
1915, 18bitri 182 . 2
209, 14, 193bitr4i 210 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-sb 1687 This theorem is referenced by:  sbcom2v2  1904
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