Description: Restricted specialization with two quantifiers, using implicit substitution. (Contributed by BJ, 2-Dec-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | rspc2gv.1 | |
|
Assertion | rspc2gv | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspc2gv.1 | |
|
2 | df-ral | |
|
3 | df-ral | |
|
4 | 3 | imbi2i | |
5 | 4 | albii | |
6 | 19.21v | |
|
7 | 6 | bicomi | |
8 | 7 | albii | |
9 | impexp | |
|
10 | eleq1 | |
|
11 | eleq1 | |
|
12 | 10 11 | bi2anan9 | |
13 | 12 1 | imbi12d | |
14 | 9 13 | bitr3id | |
15 | 14 | spc2gv | |
16 | 15 | pm2.43a | |
17 | 8 16 | syl5bi | |
18 | 5 17 | syl5bi | |
19 | 2 18 | syl5bi | |