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Mirrors > Home > MPE Home > Th. List > 3reeanv | Structured version Visualization version Unicode version |
Description: Rearrange three restricted existential quantifiers. (Contributed by Jeff Madsen, 11-Jun-2010.) |
Ref | Expression |
---|---|
3reeanv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.41v 3089 | . . 3 | |
2 | reeanv 3107 | . . . 4 | |
3 | 2 | anbi1i 731 | . . 3 |
4 | 1, 3 | bitri 264 | . 2 |
5 | df-3an 1039 | . . . . 5 | |
6 | 5 | 2rexbii 3042 | . . . 4 |
7 | reeanv 3107 | . . . 4 | |
8 | 6, 7 | bitri 264 | . . 3 |
9 | 8 | rexbii 3041 | . 2 |
10 | df-3an 1039 | . 2 | |
11 | 4, 9, 10 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 w3a 1037 wrex 2913 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-ral 2917 df-rex 2918 |
This theorem is referenced by: imasmnd2 17327 imasgrp2 17530 imasring 18619 axeuclid 25843 lshpkrlem6 34402 |
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