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Mirrors > Home > HOLE Home > Th. List > exnal | Unicode version |
Description: Theorem 19.14 of [Margaris] p. 90. |
Ref | Expression |
---|---|
exmid.1 |
Ref | Expression |
---|---|
exnal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wnot 128 | . . 3 | |
2 | wex 129 | . . . . 5 | |
3 | exmid.1 | . . . . . . 7 | |
4 | 1, 3 | wc 45 | . . . . . 6 |
5 | 4 | wl 59 | . . . . 5 |
6 | 2, 5 | wc 45 | . . . 4 |
7 | 1, 6 | wc 45 | . . 3 |
8 | 1, 7 | wc 45 | . 2 |
9 | wal 124 | . . . . 5 | |
10 | 1, 4 | wc 45 | . . . . . 6 |
11 | 10 | wl 59 | . . . . 5 |
12 | 9, 11 | wc 45 | . . . 4 |
13 | 4 | alnex 174 | . . . 4 |
14 | 12, 13 | eqcomi 70 | . . 3 |
15 | 1, 7, 14 | ceq2 80 | . 2 |
16 | 6 | notnot 187 | . 2 |
17 | 3 | wl 59 | . . . 4 |
18 | 9, 17 | wc 45 | . . 3 |
19 | 3 | notnot 187 | . . . . 5 |
20 | 3, 19 | leq 81 | . . . 4 |
21 | 9, 17, 20 | ceq2 80 | . . 3 |
22 | 1, 18, 21 | ceq2 80 | . 2 |
23 | 8, 15, 16, 22 | 3eqtr4i 86 | 1 |
Colors of variables: type var term |
Syntax hints: ht 2 hb 3 kc 5 kl 6 ke 7 kt 8 kbr 9 wffMMJ2 11 wffMMJ2t 12 tne 110 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 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-ex 121 df-or 122 |
This theorem is referenced by: (None) |
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