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Mirrors > Home > HOLE Home > Th. List > exval | Unicode version |
Description: Value of the 'there exists' predicate. |
Ref | Expression |
---|---|
alval.1 |
Ref | Expression |
---|---|
exval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wex 129 | . . 3 | |
2 | alval.1 | . . 3 | |
3 | 1, 2 | wc 45 | . 2 |
4 | df-ex 121 | . . 3 | |
5 | 1, 2, 4 | ceq1 79 | . 2 |
6 | wal 124 | . . . 4 | |
7 | wim 127 | . . . . . 6 | |
8 | wal 124 | . . . . . . 7 | |
9 | wv 58 | . . . . . . . . . 10 | |
10 | wv 58 | . . . . . . . . . 10 | |
11 | 9, 10 | wc 45 | . . . . . . . . 9 |
12 | wv 58 | . . . . . . . . 9 | |
13 | 7, 11, 12 | wov 64 | . . . . . . . 8 |
14 | 13 | wl 59 | . . . . . . 7 |
15 | 8, 14 | wc 45 | . . . . . 6 |
16 | 7, 15, 12 | wov 64 | . . . . 5 |
17 | 16 | wl 59 | . . . 4 |
18 | 6, 17 | wc 45 | . . 3 |
19 | 9, 2 | weqi 68 | . . . . . . . . . . 11 |
20 | 19 | id 25 | . . . . . . . . . 10 |
21 | 9, 10, 20 | ceq1 79 | . . . . . . . . 9 |
22 | 7, 11, 12, 21 | oveq1 89 | . . . . . . . 8 |
23 | 13, 22 | leq 81 | . . . . . . 7 |
24 | 8, 14, 23 | ceq2 80 | . . . . . 6 |
25 | 7, 15, 12, 24 | oveq1 89 | . . . . 5 |
26 | 16, 25 | leq 81 | . . . 4 |
27 | 6, 17, 26 | ceq2 80 | . . 3 |
28 | 18, 2, 27 | cl 106 | . 2 |
29 | 3, 5, 28 | eqtri 85 | 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 tim 111 tal 112 tex 113 |
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-beta 60 ax-distrc 61 ax-leq 62 ax-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 df-al 116 df-an 118 df-im 119 df-ex 121 |
This theorem is referenced by: exlimdv2 156 ax4e 158 exlimd 171 |
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