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Mirrors > Home > HOLE Home > Th. List > ax5 | Unicode version |
Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105. |
Ref | Expression |
---|---|
ax5.1 | |
ax5.2 |
Ref | Expression |
---|---|
ax5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax5.2 | . . . . . 6 | |
2 | ax5.1 | . . . . . . . 8 | |
3 | 2 | ax4 140 | . . . . . . 7 |
4 | wal 124 | . . . . . . . 8 | |
5 | wim 127 | . . . . . . . . . 10 | |
6 | 5, 2, 1 | wov 64 | . . . . . . . . 9 |
7 | 6 | wl 59 | . . . . . . . 8 |
8 | 4, 7 | wc 45 | . . . . . . 7 |
9 | 3, 8 | adantl 51 | . . . . . 6 |
10 | 6 | ax4 140 | . . . . . . 7 |
11 | 3 | ax-cb1 29 | . . . . . . 7 |
12 | 10, 11 | adantr 50 | . . . . . 6 |
13 | 1, 9, 12 | mpd 146 | . . . . 5 |
14 | wv 58 | . . . . . 6 | |
15 | 4, 14 | ax-17 95 | . . . . . . 7 |
16 | 6, 14 | ax-hbl1 93 | . . . . . . 7 |
17 | 4, 7, 14, 15, 16 | hbc 100 | . . . . . 6 |
18 | 2 | wl 59 | . . . . . . 7 |
19 | 2, 14 | ax-hbl1 93 | . . . . . . 7 |
20 | 4, 18, 14, 15, 19 | hbc 100 | . . . . . 6 |
21 | 8, 14, 11, 17, 20 | hbct 145 | . . . . 5 |
22 | 13, 21 | alrimi 170 | . . . 4 |
23 | 22 | ex 148 | . . 3 |
24 | wtru 40 | . . 3 | |
25 | 23, 24 | adantl 51 | . 2 |
26 | 25 | ex 148 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 ht 2 hb 3 kc 5 kl 6 kt 8 kbr 9 kct 10 wffMMJ2 11 wffMMJ2t 12 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-an 118 df-im 119 |
This theorem is referenced by: ax11 201 |
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