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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 921 | . . 3 | |
2 | 1 | 3exbii 1538 | . 2 |
3 | eeanv 1848 | . . 3 | |
4 | 3 | exbii 1536 | . 2 |
5 | eeanv 1848 | . . . 4 | |
6 | 5 | anbi1i 445 | . . 3 |
7 | 19.41v 1823 | . . 3 | |
8 | df-3an 921 | . . 3 | |
9 | 6, 7, 8 | 3bitr4i 210 | . 2 |
10 | 2, 4, 9 | 3bitri 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 w3a 919 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-nf 1390 |
This theorem is referenced by: vtocl3 2655 spc3egv 2689 spc3gv 2690 eloprabga 5611 prarloc 6693 |
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