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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 1997 |
. . . 4
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2 | 1 | sbbii 1775 |
. . 3
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3 | sbcom2v2 1997 |
. . 3
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4 | 2, 3 | bitri 184 |
. 2
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5 | ax-17 1536 |
. . 3
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6 | 5 | sbco2vh 1956 |
. 2
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7 | ax-17 1536 |
. . . 4
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8 | 7 | sbco2vh 1956 |
. . 3
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9 | 8 | sbbii 1775 |
. 2
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10 | 4, 6, 9 | 3bitr3i 210 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 |
This theorem is referenced by: 2sb5rf 2000 2sb6rf 2001 sbco4lem 2017 sbco4 2018 sbmo 2096 cnvopab 5044 |
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