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Mirrors > Home > ILE Home > Th. List > sbcom2v | Unicode version |
Description: Lemma for proving sbcom2 1967. It is the same as sbcom2 1967 but with additional distinct variable constraints on and , and on and . (Contributed by Jim Kingdon, 19-Feb-2018.) |
Ref | Expression |
---|---|
sbcom2v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 1458 | . . 3 | |
2 | bi2.04 247 | . . . . . 6 | |
3 | 2 | albii 1450 | . . . . 5 |
4 | 19.21v 1853 | . . . . 5 | |
5 | 3, 4 | bitri 183 | . . . 4 |
6 | 5 | albii 1450 | . . 3 |
7 | 19.21v 1853 | . . . 4 | |
8 | 7 | albii 1450 | . . 3 |
9 | 1, 6, 8 | 3bitr3i 209 | . 2 |
10 | sb6 1866 | . . 3 | |
11 | sb6 1866 | . . . . 5 | |
12 | 11 | imbi2i 225 | . . . 4 |
13 | 12 | albii 1450 | . . 3 |
14 | 10, 13 | bitri 183 | . 2 |
15 | sb6 1866 | . . 3 | |
16 | sb6 1866 | . . . . 5 | |
17 | 16 | imbi2i 225 | . . . 4 |
18 | 17 | albii 1450 | . . 3 |
19 | 15, 18 | bitri 183 | . 2 |
20 | 9, 14, 19 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1333 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-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-sb 1743 |
This theorem is referenced by: sbcom2v2 1966 |
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