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Mirrors > Home > HOLE Home > Th. List > exlimdv2 | Unicode version |
Description: Existential elimination. |
Ref | Expression |
---|---|
exlimdv2.1 | |
exlimdv2.2 |
Ref | Expression |
---|---|
exlimdv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimdv2.2 | . . 3 | |
2 | 1 | ax-cb2 30 | . 2 |
3 | 1 | ex 148 | . . . 4 |
4 | 3 | alrimiv 141 | . . 3 |
5 | wex 129 | . . . 4 | |
6 | exlimdv2.1 | . . . 4 | |
7 | 5, 6 | wc 45 | . . 3 |
8 | 4, 7 | adantr 50 | . 2 |
9 | 1 | ax-cb1 29 | . . . . . 6 |
10 | 9 | wctl 31 | . . . . 5 |
11 | 10, 7 | simpr 23 | . . . 4 |
12 | 10, 7 | wct 44 | . . . . 5 |
13 | 6 | exval 133 | . . . . 5 |
14 | 12, 13 | a1i 28 | . . . 4 |
15 | 11, 14 | mpbi 72 | . . 3 |
16 | wim 127 | . . . . 5 | |
17 | wal 124 | . . . . . 6 | |
18 | wv 58 | . . . . . . . . 9 | |
19 | 6, 18 | wc 45 | . . . . . . . 8 |
20 | wv 58 | . . . . . . . 8 | |
21 | 16, 19, 20 | wov 64 | . . . . . . 7 |
22 | 21 | wl 59 | . . . . . 6 |
23 | 17, 22 | wc 45 | . . . . 5 |
24 | 16, 23, 20 | wov 64 | . . . 4 |
25 | 20, 2 | weqi 68 | . . . . . . . . 9 |
26 | 25 | id 25 | . . . . . . . 8 |
27 | 16, 19, 20, 26 | oveq2 91 | . . . . . . 7 |
28 | 21, 27 | leq 81 | . . . . . 6 |
29 | 17, 22, 28 | ceq2 80 | . . . . 5 |
30 | 16, 23, 20, 29, 26 | oveq12 90 | . . . 4 |
31 | 24, 2, 30 | cla4v 142 | . . 3 |
32 | 15, 31 | syl 16 | . 2 |
33 | 2, 8, 32 | mpd 146 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 hb 3 kc 5 kl 6 ke 7 kbr 9 kct 10 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-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: exlimdv 157 dfex2 185 |
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