Description: Value of the structure replacement function. (Contributed by Mario Carneiro, 30-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | setsvalg | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex | |
|
2 | elex | |
|
3 | resexg | |
|
4 | 3 | adantr | |
5 | snex | |
|
6 | unexg | |
|
7 | 4 5 6 | sylancl | |
8 | simpl | |
|
9 | simpr | |
|
10 | 9 | sneqd | |
11 | 10 | dmeqd | |
12 | 11 | difeq2d | |
13 | 8 12 | reseq12d | |
14 | 13 10 | uneq12d | |
15 | df-sets | |
|
16 | 14 15 | ovmpoga | |
17 | 7 16 | mpd3an3 | |
18 | 1 2 17 | syl2an | |