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Theorem sbco4 2186
 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 2158 . . 3
2 nfv 1674 . . . . 5
32sbco2 2118 . . . 4
43sbbii 1709 . . 3
51, 4bitr3i 251 . 2
6 sbco4lem 2185 . 2
7 sbco4lem 2185 . 2
85, 6, 73bitri 271 1
 Colors of variables: wff setvar class Syntax hints:   wb 184  wsb 1702 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1588  df-nf 1591  df-sb 1703 This theorem is referenced by: (None)
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