Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > spc2ed | Structured version Visualization version Unicode version |
Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by Thierry Arnoux, 23-Aug-2017.) |
Ref | Expression |
---|---|
spc2ed.x | |
spc2ed.y | |
spc2ed.1 |
Ref | Expression |
---|---|
spc2ed |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 3215 | . . . 4 | |
2 | elisset 3215 | . . . 4 | |
3 | 1, 2 | anim12i 590 | . . 3 |
4 | eeanv 2182 | . . 3 | |
5 | 3, 4 | sylibr 224 | . 2 |
6 | nfv 1843 | . . . . 5 | |
7 | spc2ed.x | . . . . 5 | |
8 | 6, 7 | nfan 1828 | . . . 4 |
9 | nfv 1843 | . . . . . 6 | |
10 | spc2ed.y | . . . . . 6 | |
11 | 9, 10 | nfan 1828 | . . . . 5 |
12 | anass 681 | . . . . . . . 8 | |
13 | ancom 466 | . . . . . . . . 9 | |
14 | 13 | anbi1i 731 | . . . . . . . 8 |
15 | 12, 14 | bitr3i 266 | . . . . . . 7 |
16 | spc2ed.1 | . . . . . . . 8 | |
17 | 16 | biimparc 504 | . . . . . . 7 |
18 | 15, 17 | sylbir 225 | . . . . . 6 |
19 | 18 | ex 450 | . . . . 5 |
20 | 11, 19 | eximd 2085 | . . . 4 |
21 | 8, 20 | eximd 2085 | . . 3 |
22 | 21 | impancom 456 | . 2 |
23 | 5, 22 | sylan2 491 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wnf 1708 wcel 1990 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: spc2d 29313 cnvoprab 29498 |
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