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Theorem sbco4 2210
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:   , ,   , ,   , ,   ,   ,   ,

Proof of Theorem sbco4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcom2 2189 . . 3
2 nfv 1707 . . . . 5
32sbco2 2158 . . . 4
43sbbii 1746 . . 3
51, 4bitr3i 251 . 2
6 sbco4lem 2209 . 2
7 sbco4lem 2209 . 2
85, 6, 73bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  [wsb 1739
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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