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Mirrors > Home > HOLE Home > Th. List > hbxfrf | Unicode version |
Description: Transfer a hypothesis builder to an equivalent expression. |
Ref | Expression |
---|---|
hbxfr.1 | |
hbxfr.2 | |
hbxfrf.3 | |
hbxfrf.4 |
Ref | Expression |
---|---|
hbxfrf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbxfr.1 | . . . . 5 | |
2 | hbxfrf.3 | . . . . 5 | |
3 | 1, 2 | eqtypi 69 | . . . 4 |
4 | 3 | wl 59 | . . 3 |
5 | hbxfr.2 | . . 3 | |
6 | 4, 5 | wc 45 | . 2 |
7 | hbxfrf.4 | . 2 | |
8 | 1 | wl 59 | . . . 4 |
9 | 1, 2 | leq 81 | . . . 4 |
10 | 8, 5, 9 | ceq1 79 | . . 3 |
11 | 7 | ax-cb1 29 | . . . 4 |
12 | 11 | wctl 31 | . . 3 |
13 | 10, 12 | adantl 51 | . 2 |
14 | 2, 12 | adantl 51 | . 2 |
15 | 6, 7, 13, 14 | 3eqtr4i 86 | 1 |
Colors of variables: type var term |
Syntax hints: kc 5 kl 6 ke 7 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ceq 46 ax-leq 62 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: hbxfr 98 hbov 101 hbct 145 |
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