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Mirrors > Home > ILE Home > Th. List > sbcocom | Unicode version |
Description: Relationship between composition and commutativity for substitution. (Contributed by Jim Kingdon, 28-Feb-2018.) |
Ref | Expression |
---|---|
sbcocom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsb1 1668 | . . 3 | |
2 | sbequ 1721 | . . . 4 | |
3 | 2 | sbimi 1647 | . . 3 |
4 | 1, 3 | ax-mp 7 | . 2 |
5 | sbbi 1833 | . 2 | |
6 | 4, 5 | mpbi 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wsb 1645 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sbcomv 1845 sbco3xzyz 1847 sbcom 1849 |
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