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Mirrors > Home > ILE Home > Th. List > sbal1yz | Unicode version |
Description: Lemma for proving sbal1 1978. Same as sbal1 1978 but with an additional disjoint variable condition on . (Contributed by Jim Kingdon, 23-Feb-2018.) |
Ref | Expression |
---|---|
sbal1yz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dveeq2or 1789 | . . . . . 6 | |
2 | equcom 1683 | . . . . . . . . 9 | |
3 | 2 | nfbii 1450 | . . . . . . . 8 |
4 | 19.21t 1562 | . . . . . . . 8 | |
5 | 3, 4 | sylbi 120 | . . . . . . 7 |
6 | 5 | orim2i 751 | . . . . . 6 |
7 | 1, 6 | ax-mp 5 | . . . . 5 |
8 | 7 | ori 713 | . . . 4 |
9 | 8 | albidv 1797 | . . 3 |
10 | alcom 1455 | . . . 4 | |
11 | sb6 1859 | . . . . . 6 | |
12 | 2 | imbi1i 237 | . . . . . . 7 |
13 | 12 | albii 1447 | . . . . . 6 |
14 | 11, 13 | bitri 183 | . . . . 5 |
15 | 14 | albii 1447 | . . . 4 |
16 | 10, 15 | bitr4i 186 | . . 3 |
17 | sb6 1859 | . . . 4 | |
18 | 2 | imbi1i 237 | . . . . 5 |
19 | 18 | albii 1447 | . . . 4 |
20 | 17, 19 | bitr2i 184 | . . 3 |
21 | 9, 16, 20 | 3bitr3g 221 | . 2 |
22 | 21 | bicomd 140 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 698 wal 1330 wnf 1437 wsb 1736 |
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-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 |
This theorem is referenced by: sbal1 1978 |
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