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Mirrors > Home > HOLE Home > Th. List > ceq12 | Unicode version |
Description: Equality theorem for combination. |
Ref | Expression |
---|---|
ceq12.1 | |
ceq12.2 | |
ceq12.3 | |
ceq12.4 |
Ref | Expression |
---|---|
ceq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | weq 38 | . 2 | |
2 | ceq12.1 | . . 3 | |
3 | ceq12.2 | . . 3 | |
4 | 2, 3 | wc 45 | . 2 |
5 | ceq12.3 | . . . 4 | |
6 | 2, 5 | eqtypi 69 | . . 3 |
7 | ceq12.4 | . . . 4 | |
8 | 3, 7 | eqtypi 69 | . . 3 |
9 | 6, 8 | wc 45 | . 2 |
10 | weq 38 | . . . 4 | |
11 | 10, 2, 6, 5 | dfov1 66 | . . 3 |
12 | weq 38 | . . . 4 | |
13 | 12, 3, 8, 7 | dfov1 66 | . . 3 |
14 | 2, 6, 3, 8 | ax-ceq 46 | . . 3 |
15 | 11, 13, 14 | syl2anc 19 | . 2 |
16 | 1, 4, 9, 15 | dfov2 67 | 1 |
Colors of variables: type var term |
Syntax hints: ht 2 kc 5 ke 7 kbr 9 wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ceq 46 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: ceq1 79 ceq2 80 oveq123 88 hbc 100 ac 184 |
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