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Mirrors > Home > ILE Home > Th. List > sbcom2 | Unicode version |
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.) |
Ref | Expression |
---|---|
sbcom2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcom2v2 1937 |
. . . 4
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2 | 1 | sbbii 1721 |
. . 3
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3 | sbcom2v2 1937 |
. . 3
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4 | 2, 3 | bitri 183 |
. 2
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5 | ax-17 1489 |
. . 3
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6 | 5 | sbco2v 1896 |
. 2
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7 | ax-17 1489 |
. . . 4
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8 | 7 | sbco2v 1896 |
. . 3
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9 | 8 | sbbii 1721 |
. 2
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10 | 4, 6, 9 | 3bitr3i 209 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 |
This theorem depends on definitions: df-bi 116 df-nf 1420 df-sb 1719 |
This theorem is referenced by: 2sb5rf 1940 2sb6rf 1941 sbco4lem 1957 sbco4 1958 sbmo 2034 cnvopab 4898 |
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