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Mirrors > Home > ILE Home > Th. List > ax11ev | Unicode version |
Description: Analogue to ax11v 1820 for existential quantification. (Contributed by Jim Kingdon, 9-Jan-2018.) |
Ref | Expression |
---|---|
ax11ev |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1689 | . 2 | |
2 | ax11e 1789 | . . . . 5 | |
3 | ax-17 1519 | . . . . . 6 | |
4 | 3 | 19.9h 1636 | . . . . 5 |
5 | 2, 4 | syl6ib 160 | . . . 4 |
6 | equequ2 1706 | . . . . 5 | |
7 | 6 | anbi1d 462 | . . . . . . 7 |
8 | 7 | exbidv 1818 | . . . . . 6 |
9 | 8 | imbi1d 230 | . . . . 5 |
10 | 6, 9 | imbi12d 233 | . . . 4 |
11 | 5, 10 | mpbii 147 | . . 3 |
12 | 11 | exlimiv 1591 | . 2 |
13 | 1, 12 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wex 1485 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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