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Mirrors > Home > HOLE Home > Th. List > exlimdv | Unicode version |
Description: Existential elimination. |
Ref | Expression |
---|---|
exlimdv.1 |
Ref | Expression |
---|---|
exlimdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimdv.1 | . . . . 5 | |
2 | 1 | ax-cb1 29 | . . . 4 |
3 | 2 | wctr 32 | . . 3 |
4 | 3 | wl 59 | . 2 |
5 | wv 58 | . . . 4 | |
6 | 4, 5 | wc 45 | . . 3 |
7 | 1 | ax-cb2 30 | . . 3 |
8 | wim 127 | . . . . 5 | |
9 | 8, 6, 7 | wov 64 | . . . 4 |
10 | 1 | ex 148 | . . . 4 |
11 | wv 58 | . . . . 5 | |
12 | 8, 11 | ax-17 95 | . . . . 5 |
13 | 3, 11 | ax-hbl1 93 | . . . . . 6 |
14 | 5, 11 | ax-17 95 | . . . . . 6 |
15 | 4, 5, 11, 13, 14 | hbc 100 | . . . . 5 |
16 | 7, 11 | ax-17 95 | . . . . 5 |
17 | 8, 6, 11, 7, 12, 15, 16 | hbov 101 | . . . 4 |
18 | wv 58 | . . . . . . . 8 | |
19 | 18, 5 | weqi 68 | . . . . . . 7 |
20 | 4, 18 | wc 45 | . . . . . . . 8 |
21 | 3 | beta 82 | . . . . . . . 8 |
22 | 20, 21 | eqcomi 70 | . . . . . . 7 |
23 | 19, 22 | a1i 28 | . . . . . 6 |
24 | 19 | id 25 | . . . . . . 7 |
25 | 4, 18, 24 | ceq2 80 | . . . . . 6 |
26 | 3, 23, 25 | eqtri 85 | . . . . 5 |
27 | 8, 3, 7, 26 | oveq1 89 | . . . 4 |
28 | 5, 9, 10, 17, 27 | insti 104 | . . 3 |
29 | 6, 7, 28 | imp 147 | . 2 |
30 | 4, 29 | exlimdv2 156 | 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 kct 10 wffMMJ2 11 tim 111 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-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 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: (None) |
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