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Mirrors > Home > NFE 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 936 | . . 3 | |
2 | 1 | 3exbii 1584 | . 2 |
3 | eeanv 1913 | . . 3 | |
4 | 3 | exbii 1582 | . 2 |
5 | eeanv 1913 | . . . 4 | |
6 | 5 | anbi1i 676 | . . 3 |
7 | 19.41v 1901 | . . 3 | |
8 | df-3an 936 | . . 3 | |
9 | 6, 7, 8 | 3bitr4i 268 | . 2 |
10 | 2, 4, 9 | 3bitri 262 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wa 358 w3a 934 wex 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 df-ex 1542 df-nf 1545 |
This theorem is referenced by: vtocl3 2911 spc3egv 2943 eloprabga 5578 mucass 6135 taddc 6229 letc 6231 |
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