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Mirrors > Home > HOLE Home > Th. List > ax3 | Unicode version |
Description: Axiom Transp. Axiom A3 of [Margaris] p. 49. |
Ref | Expression |
---|---|
ax3.1 | |
ax3.2 |
Ref | Expression |
---|---|
ax3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax3.1 | . . . . 5 | |
2 | wnot 128 | . . . . . 6 | |
3 | 2, 1 | wc 45 | . . . . 5 |
4 | wim 127 | . . . . . . . 8 | |
5 | ax3.2 | . . . . . . . . 9 | |
6 | 2, 5 | wc 45 | . . . . . . . 8 |
7 | 4, 3, 6 | wov 64 | . . . . . . 7 |
8 | 7, 5 | wct 44 | . . . . . 6 |
9 | 1 | exmid 186 | . . . . . 6 |
10 | 8, 9 | a1i 28 | . . . . 5 |
11 | 10 | ax-cb1 29 | . . . . . 6 |
12 | 11, 1 | simpr 23 | . . . . 5 |
13 | wfal 125 | . . . . . . . 8 | |
14 | 7 | id 25 | . . . . . . . . . 10 |
15 | 3, 6, 14 | imp 147 | . . . . . . . . 9 |
16 | 15 | ax-cb1 29 | . . . . . . . . . 10 |
17 | 5 | notval 135 | . . . . . . . . . 10 |
18 | 16, 17 | a1i 28 | . . . . . . . . 9 |
19 | 15, 18 | mpbi 72 | . . . . . . . 8 |
20 | 5, 13, 19 | imp 147 | . . . . . . 7 |
21 | 20 | an32s 55 | . . . . . 6 |
22 | 1 | pm2.21 143 | . . . . . 6 |
23 | 21, 22 | syl 16 | . . . . 5 |
24 | 1, 3, 1, 10, 12, 23 | ecase 153 | . . . 4 |
25 | 24 | ex 148 | . . 3 |
26 | wtru 40 | . . 3 | |
27 | 25, 26 | adantl 51 | . 2 |
28 | 27 | ex 148 | 1 |
Colors of variables: type var term |
Syntax hints: hb 3 kc 5 ke 7 kt 8 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 tfal 108 tne 110 tim 111 tor 114 |
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-ac 183 |
This theorem depends on definitions: df-ov 65 df-al 116 df-fal 117 df-an 118 df-im 119 df-not 120 df-or 122 |
This theorem is referenced by: (None) |
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