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Mirrors > Home > ILE Home > Th. List > dveeq2 | Unicode version |
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.) |
Ref | Expression |
---|---|
dveeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-i12 1398 | . . . . 5 | |
2 | orcom 647 | . . . . . 6 | |
3 | 2 | orbi2i 679 | . . . . 5 |
4 | 1, 3 | mpbi 133 | . . . 4 |
5 | orass 684 | . . . 4 | |
6 | 4, 5 | mpbir 134 | . . 3 |
7 | orel2 645 | . . 3 | |
8 | 6, 7 | mpi 15 | . 2 |
9 | ax16 1694 | . . 3 | |
10 | sp 1401 | . . 3 | |
11 | 9, 10 | jaoi 636 | . 2 |
12 | 8, 11 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 629 wal 1241 |
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-in2 545 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 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: nd5 1699 ax11v2 1701 dveeq1 1895 |
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