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Mirrors > Home > HOLE Home > Th. List > ax12 | Unicode version |
Description: Axiom of Quantifier Introduction. Axiom scheme C9' in [Megill] p. 448 (p. 16 of the preprint). |
Ref | Expression |
---|---|
ax12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wv 58 | . . . . . . 7 | |
2 | wv 58 | . . . . . . 7 | |
3 | 1, 2 | weqi 68 | . . . . . 6 |
4 | wv 58 | . . . . . . 7 | |
5 | 3, 4 | ax-17 95 | . . . . . 6 |
6 | 3, 5 | isfree 176 | . . . . 5 |
7 | wnot 128 | . . . . . 6 | |
8 | wal 124 | . . . . . . 7 | |
9 | wv 58 | . . . . . . . . 9 | |
10 | 9, 2 | weqi 68 | . . . . . . . 8 |
11 | 10 | wl 59 | . . . . . . 7 |
12 | 8, 11 | wc 45 | . . . . . 6 |
13 | 7, 12 | wc 45 | . . . . 5 |
14 | 6, 13 | adantr 50 | . . . 4 |
15 | 14 | ex 148 | . . 3 |
16 | 9, 1 | weqi 68 | . . . . . 6 |
17 | 16 | wl 59 | . . . . 5 |
18 | 8, 17 | wc 45 | . . . 4 |
19 | 7, 18 | wc 45 | . . 3 |
20 | 15, 19 | adantr 50 | . 2 |
21 | 20 | ex 148 | 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 tne 110 tim 111 tal 112 |
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 |
This theorem is referenced by: (None) |
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