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Mirrors > Home > MPE Home > Th. List > rspc2gv | Structured version Visualization version Unicode version |
Description: Restricted specialization with two quantifiers, using implicit substitution. (Contributed by BJ, 2-Dec-2021.) |
Ref | Expression |
---|---|
rspc2gv.1 |
Ref | Expression |
---|---|
rspc2gv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2917 | . 2 | |
2 | df-ral 2917 | . . . . 5 | |
3 | 2 | imbi2i 326 | . . . 4 |
4 | 3 | albii 1747 | . . 3 |
5 | 19.21v 1868 | . . . . . 6 | |
6 | 5 | bicomi 214 | . . . . 5 |
7 | 6 | albii 1747 | . . . 4 |
8 | impexp 462 | . . . . . . 7 | |
9 | eleq1 2689 | . . . . . . . . 9 | |
10 | eleq1 2689 | . . . . . . . . 9 | |
11 | 9, 10 | bi2anan9 917 | . . . . . . . 8 |
12 | rspc2gv.1 | . . . . . . . 8 | |
13 | 11, 12 | imbi12d 334 | . . . . . . 7 |
14 | 8, 13 | syl5bbr 274 | . . . . . 6 |
15 | 14 | spc2gv 3296 | . . . . 5 |
16 | 15 | pm2.43a 54 | . . . 4 |
17 | 7, 16 | syl5bi 232 | . . 3 |
18 | 4, 17 | syl5bi 232 | . 2 |
19 | 1, 18 | syl5bi 232 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wceq 1483 wcel 1990 wral 2912 |
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-ral 2917 df-v 3202 |
This theorem is referenced by: eulplig 27337 |
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