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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 969 | . . 3 | |
2 | 1 | 3exbii 1594 | . 2 |
3 | eeanv 1919 | . . 3 | |
4 | 3 | exbii 1592 | . 2 |
5 | eeanv 1919 | . . . 4 | |
6 | 5 | anbi1i 454 | . . 3 |
7 | 19.41v 1889 | . . 3 | |
8 | df-3an 969 | . . 3 | |
9 | 6, 7, 8 | 3bitr4i 211 | . 2 |
10 | 2, 4, 9 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 967 wex 1479 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-nf 1448 |
This theorem is referenced by: vtocl3 2777 spc3egv 2813 spc3gv 2814 eloprabga 5920 prarloc 7435 |
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