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Mirrors > Home > HOLE Home > Th. List > hbov | Unicode version |
Description: Hypothesis builder for binary operation. |
Ref | Expression |
---|---|
hbov.1 | |
hbov.2 | |
hbov.3 | |
hbov.4 | |
hbov.5 | |
hbov.6 | |
hbov.7 |
Ref | Expression |
---|---|
hbov |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbov.5 | . . . 4 | |
2 | 1 | ax-cb1 29 | . . 3 |
3 | 2 | trud 27 | . 2 |
4 | hbov.1 | . . . 4 | |
5 | hbov.2 | . . . 4 | |
6 | hbov.4 | . . . 4 | |
7 | 4, 5, 6 | wov 64 | . . 3 |
8 | hbov.3 | . . 3 | |
9 | weq 38 | . . . 4 | |
10 | 4, 5 | wc 45 | . . . . 5 |
11 | 10, 6 | wc 45 | . . . 4 |
12 | 4, 5, 6 | df-ov 65 | . . . 4 |
13 | 9, 7, 11, 12 | dfov2 67 | . . 3 |
14 | hbov.6 | . . . . . 6 | |
15 | 4, 5, 8, 1, 14 | hbc 100 | . . . . 5 |
16 | hbov.7 | . . . . 5 | |
17 | 10, 6, 8, 15, 16 | hbc 100 | . . . 4 |
18 | wtru 40 | . . . 4 | |
19 | 17, 18 | adantr 50 | . . 3 |
20 | 7, 8, 13, 19 | hbxfrf 97 | . 2 |
21 | 3, 20 | mpdan 33 | 1 |
Colors of variables: type var term |
Syntax hints: ht 2 kc 5 kl 6 ke 7 kt 8 kbr 9 wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ceq 46 ax-distrc 61 ax-leq 62 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: clf 105 hbct 145 exlimdv 157 cbvf 167 leqf 169 exlimd 171 exmid 186 axrep 207 |
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