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Theorem sbco4 1926
 Description: Two ways of exchanging two variables. Both sides of the biconditional exchange and , either via two temporary variables and , or a single temporary . (Contributed by Jim Kingdon, 25-Sep-2018.)
Assertion
Ref Expression
sbco4
Distinct variable groups:   ,,   ,,   ,,   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem sbco4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcom2 1906 . . 3
2 nfv 1462 . . . . 5
32sbco2 1882 . . . 4
43sbbii 1690 . . 3
51, 4bitr3i 184 . 2
6 sbco4lem 1925 . 2
7 sbco4lem 1925 . 2
85, 6, 73bitri 204 1
 Colors of variables: wff set class Syntax hints:   wb 103  wsb 1687 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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688 This theorem is referenced by: (None)
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