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Mirrors > Home > HOLE Home > Th. List > ax4g | Unicode version |
Description: If is true for all , then it is true for . |
Ref | Expression |
---|---|
ax4g.1 | |
ax4g.2 |
Ref | Expression |
---|---|
ax4g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wal 124 | . . . 4 | |
2 | ax4g.1 | . . . 4 | |
3 | 1, 2 | wc 45 | . . 3 |
4 | 3 | trud 27 | . 2 |
5 | ax4g.2 | . . . 4 | |
6 | 2, 5 | wc 45 | . . 3 |
7 | 4 | ax-cb1 29 | . . . . . 6 |
8 | 7 | id 25 | . . . . 5 |
9 | 2 | alval 132 | . . . . . 6 |
10 | 7, 9 | a1i 28 | . . . . 5 |
11 | 8, 10 | mpbi 72 | . . . 4 |
12 | 2, 5, 11 | ceq1 79 | . . 3 |
13 | 5, 4 | hbth 99 | . . 3 |
14 | 6, 12, 13 | eqtri 85 | . 2 |
15 | 4, 14 | mpbir 77 | 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 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-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 df-al 116 |
This theorem is referenced by: ax4 140 cla4v 142 |
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