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Mirrors > Home > ILE Home > Th. List > eeeanv | Unicode version |
Description: Rearrange existential quantifiers. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
eeeanv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 887 | . . 3 | |
2 | 1 | 3exbii 1498 | . 2 |
3 | eeanv 1807 | . . 3 | |
4 | 3 | exbii 1496 | . 2 |
5 | eeanv 1807 | . . . 4 | |
6 | 5 | anbi1i 431 | . . 3 |
7 | 19.41v 1782 | . . 3 | |
8 | df-3an 887 | . . 3 | |
9 | 6, 7, 8 | 3bitr4i 201 | . 2 |
10 | 2, 4, 9 | 3bitri 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 w3a 885 wex 1381 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 |
This theorem is referenced by: vtocl3 2610 spc3egv 2644 spc3gv 2645 eloprabga 5591 prarloc 6601 |
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