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Mirrors > Home > HOLE Home > Th. List > leqf | Unicode version |
Description: Equality theorem for lambda abstraction, using bound variable instead of distinct variables. |
Ref | Expression |
---|---|
leqf.1 | |
leqf.2 | |
leqf.3 |
Ref | Expression |
---|---|
leqf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leqf.1 | . . . . 5 | |
2 | 1 | wl 59 | . . . 4 |
3 | wv 58 | . . . 4 | |
4 | 2, 3 | wc 45 | . . 3 |
5 | 4 | wl 59 | . 2 |
6 | leqf.2 | . . . . 5 | |
7 | 6 | ax-cb1 29 | . . . . . 6 |
8 | 1 | beta 82 | . . . . . 6 |
9 | 7, 8 | a1i 28 | . . . . 5 |
10 | 1, 6 | eqtypi 69 | . . . . . . 7 |
11 | 10 | beta 82 | . . . . . 6 |
12 | 7, 11 | a1i 28 | . . . . 5 |
13 | 1, 6, 9, 12 | 3eqtr4i 86 | . . . 4 |
14 | weq 38 | . . . . 5 | |
15 | wv 58 | . . . . 5 | |
16 | 10 | wl 59 | . . . . . 6 |
17 | 16, 3 | wc 45 | . . . . 5 |
18 | 14, 15 | ax-17 95 | . . . . 5 |
19 | 1, 15 | ax-hbl1 93 | . . . . . 6 |
20 | 3, 15 | ax-17 95 | . . . . . 6 |
21 | 2, 3, 15, 19, 20 | hbc 100 | . . . . 5 |
22 | 10, 15 | ax-hbl1 93 | . . . . . 6 |
23 | 16, 3, 15, 22, 20 | hbc 100 | . . . . 5 |
24 | 14, 4, 15, 17, 18, 21, 23 | hbov 101 | . . . 4 |
25 | leqf.3 | . . . 4 | |
26 | wv 58 | . . . . . 6 | |
27 | 2, 26 | wc 45 | . . . . 5 |
28 | 16, 26 | wc 45 | . . . . 5 |
29 | 26, 3 | weqi 68 | . . . . . . 7 |
30 | 29 | id 25 | . . . . . 6 |
31 | 2, 26, 30 | ceq2 80 | . . . . 5 |
32 | 16, 26, 30 | ceq2 80 | . . . . 5 |
33 | 14, 27, 28, 31, 32 | oveq12 90 | . . . 4 |
34 | 29, 7 | eqid 73 | . . . 4 |
35 | 13, 24, 25, 33, 34 | ax-inst 103 | . . 3 |
36 | 4, 35 | leq 81 | . 2 |
37 | 2 | eta 166 | . . 3 |
38 | 7, 37 | a1i 28 | . 2 |
39 | 16 | eta 166 | . . 3 |
40 | 7, 39 | a1i 28 | . 2 |
41 | 5, 36, 38, 40 | 3eqtr3i 87 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 hb 3 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-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-hbl1 93 ax-17 95 ax-inst 103 ax-eta 165 |
This theorem depends on definitions: df-ov 65 df-al 116 |
This theorem is referenced by: alrimi 170 axext 206 axrep 207 |
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