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Mirrors > Home > ILE Home > Th. List > dveeq2or | Unicode version |
Description: Quantifier introduction when one pair of variables is distinct. Like dveeq2 1788 but connecting by a disjunction rather than negation and implication makes the theorem stronger in intuitionistic logic. (Contributed by Jim Kingdon, 1-Feb-2018.) |
Ref | Expression |
---|---|
dveeq2or |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-i12 1486 | . . . . . 6 | |
2 | orass 757 | . . . . . 6 | |
3 | 1, 2 | mpbir 145 | . . . . 5 |
4 | pm1.4 717 | . . . . . 6 | |
5 | 4 | orim1i 750 | . . . . 5 |
6 | 3, 5 | ax-mp 5 | . . . 4 |
7 | orass 757 | . . . 4 | |
8 | 6, 7 | mpbi 144 | . . 3 |
9 | ax16 1786 | . . . . . 6 | |
10 | 9 | a5i 1523 | . . . . 5 |
11 | id 19 | . . . . 5 | |
12 | 10, 11 | jaoi 706 | . . . 4 |
13 | 12 | orim2i 751 | . . 3 |
14 | 8, 13 | ax-mp 5 | . 2 |
15 | df-nf 1438 | . . . 4 | |
16 | 15 | biimpri 132 | . . 3 |
17 | 16 | orim2i 751 | . 2 |
18 | 14, 17 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 698 wal 1330 wnf 1437 |
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-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 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 |
This theorem is referenced by: equs5or 1803 sbal1yz 1977 copsexg 4174 |
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