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Mirrors > Home > HOLE Home > Th. List > alnex | Unicode version |
Description: Theorem 19.7 of [Margaris] p. 89. |
Ref | Expression |
---|---|
alnex1.1 |
Ref | Expression |
---|---|
alnex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alnex1.1 | . . . . . 6 | |
2 | wfal 125 | . . . . . 6 | |
3 | wnot 128 | . . . . . . . . 9 | |
4 | 3, 1 | wc 45 | . . . . . . . 8 |
5 | 4 | ax4 140 | . . . . . . 7 |
6 | 5 | ax-cb1 29 | . . . . . . . 8 |
7 | 1 | notval 135 | . . . . . . . 8 |
8 | 6, 7 | a1i 28 | . . . . . . 7 |
9 | 5, 8 | mpbi 72 | . . . . . 6 |
10 | 1, 2, 9 | imp 147 | . . . . 5 |
11 | wal 124 | . . . . . 6 | |
12 | 4 | wl 59 | . . . . . 6 |
13 | wv 58 | . . . . . 6 | |
14 | 11, 13 | ax-17 95 | . . . . . 6 |
15 | 4, 13 | ax-hbl1 93 | . . . . . 6 |
16 | 11, 12, 13, 14, 15 | hbc 100 | . . . . 5 |
17 | 2, 13 | ax-17 95 | . . . . 5 |
18 | 10, 16, 17 | exlimd 171 | . . . 4 |
19 | 18 | ex 148 | . . 3 |
20 | wex 129 | . . . . . 6 | |
21 | 1 | wl 59 | . . . . . 6 |
22 | 20, 21 | wc 45 | . . . . 5 |
23 | 22 | notval 135 | . . . 4 |
24 | 6, 23 | a1i 28 | . . 3 |
25 | 19, 24 | mpbir 77 | . 2 |
26 | 1 | 19.8a 160 | . . . . . 6 |
27 | wtru 40 | . . . . . 6 | |
28 | 26, 27 | adantl 51 | . . . . 5 |
29 | 28 | con3d 152 | . . . 4 |
30 | 29 | trul 37 | . . 3 |
31 | 3, 13 | ax-17 95 | . . . 4 |
32 | 20, 13 | ax-17 95 | . . . . 5 |
33 | 1, 13 | ax-hbl1 93 | . . . . 5 |
34 | 20, 21, 13, 32, 33 | hbc 100 | . . . 4 |
35 | 3, 22, 13, 31, 34 | hbc 100 | . . 3 |
36 | 30, 35 | alrimi 170 | . 2 |
37 | 25, 36 | dedi 75 | 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 tfal 108 tne 110 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 ax-eta 165 |
This theorem depends on definitions: df-ov 65 df-al 116 df-fal 117 df-an 118 df-im 119 df-not 120 df-ex 121 |
This theorem is referenced by: exnal1 175 exnal 188 ax9 199 |
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