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Theorem sbco3xzyz 1847
 Description: Version of sbco3 1848 with distinct variable constraints between and , and and . Lemma for proving sbco3 1848. (Contributed by Jim Kingdon, 22-Mar-2018.)
Assertion
Ref Expression
sbco3xzyz
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbco3xzyz
StepHypRef Expression
1 sbcomxyyz 1846 . 2
2 sbcocom 1844 . 2
3 sbcocom 1844 . 2
41, 2, 33bitr4i 201 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-bndl 1399  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:  sbco3  1848
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