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Mirrors > Home > HOLE Home > Th. List > ax6 | Unicode version |
Description: Axiom of Quantified Negation. Axiom C5-2 of [Monk2] p. 113. |
Ref | Expression |
---|---|
ax6.1 |
Ref | Expression |
---|---|
ax6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wnot 128 | . . 3 | |
2 | wal 124 | . . . 4 | |
3 | ax6.1 | . . . . 5 | |
4 | 3 | wl 59 | . . . 4 |
5 | 2, 4 | wc 45 | . . 3 |
6 | 1, 5 | wc 45 | . 2 |
7 | wv 58 | . . 3 | |
8 | 1, 7 | ax-17 95 | . . 3 |
9 | 2, 7 | ax-17 95 | . . . 4 |
10 | 3, 7 | ax-hbl1 93 | . . . 4 |
11 | 2, 4, 7, 9, 10 | hbc 100 | . . 3 |
12 | 1, 5, 7, 8, 11 | hbc 100 | . 2 |
13 | 6, 12 | isfree 176 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 hb 3 kc 5 kl 6 kt 8 kbr 9 wffMMJ2 11 wffMMJ2t 12 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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