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Mirrors > Home > HOLE Home > Th. List > ax4e | Unicode version |
Description: Existential introduction. |
Ref | Expression |
---|---|
ax4e.1 | |
ax4e.2 |
Ref | Expression |
---|---|
ax4e |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wv 58 | . . . . 5 | |
2 | ax4e.1 | . . . . . . 7 | |
3 | ax4e.2 | . . . . . . 7 | |
4 | 2, 3 | wc 45 | . . . . . 6 |
5 | wal 124 | . . . . . . 7 | |
6 | wim 127 | . . . . . . . . 9 | |
7 | wv 58 | . . . . . . . . . 10 | |
8 | 2, 7 | wc 45 | . . . . . . . . 9 |
9 | 6, 8, 1 | wov 64 | . . . . . . . 8 |
10 | 9 | wl 59 | . . . . . . 7 |
11 | 5, 10 | wc 45 | . . . . . 6 |
12 | 4, 11 | simpl 22 | . . . . 5 |
13 | 7, 3 | weqi 68 | . . . . . . . . . 10 |
14 | 13 | id 25 | . . . . . . . . 9 |
15 | 2, 7, 14 | ceq2 80 | . . . . . . . 8 |
16 | 6, 8, 1, 15 | oveq1 89 | . . . . . . 7 |
17 | 9, 3, 16 | cla4v 142 | . . . . . 6 |
18 | 17, 4 | adantl 51 | . . . . 5 |
19 | 1, 12, 18 | mpd 146 | . . . 4 |
20 | 19 | ex 148 | . . 3 |
21 | 20 | alrimiv 141 | . 2 |
22 | 2 | exval 133 | . . 3 |
23 | 4, 22 | a1i 28 | . 2 |
24 | 21, 23 | mpbir 77 | 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: cla4ev 159 19.8a 160 dfex2 185 axrep 207 |
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