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Theorem sbcom2 1967
 Description: Commutativity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 27-May-1997.) (Proof modified to be intuitionistic by Jim Kingdon, 19-Feb-2018.)
Assertion
Ref Expression
sbcom2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem sbcom2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcom2v2 1966 . . . 4
21sbbii 1745 . . 3
3 sbcom2v2 1966 . . 3
42, 3bitri 183 . 2
5 ax-17 1506 . . 3
65sbco2vh 1925 . 2
7 ax-17 1506 . . . 4
87sbco2vh 1925 . . 3
98sbbii 1745 . 2
104, 6, 93bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wb 104  wsb 1742 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743 This theorem is referenced by:  2sb5rf  1969  2sb6rf  1970  sbco4lem  1986  sbco4  1987  sbmo  2065  cnvopab  4986
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