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Mirrors > Home > HOLE Home > Th. List > alrimi | Unicode version |
Description: If one can prove where does not contain , then is true for all . |
Ref | Expression |
---|---|
alrimi.1 | |
alrimi.2 |
Ref | Expression |
---|---|
alrimi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimi.1 | . . . 4 | |
2 | 1 | ax-cb2 30 | . . 3 |
3 | wtru 40 | . . . 4 | |
4 | 1 | eqtru 76 | . . . 4 |
5 | 3, 4 | eqcomi 70 | . . 3 |
6 | alrimi.2 | . . 3 | |
7 | 2, 5, 6 | leqf 169 | . 2 |
8 | 1 | ax-cb1 29 | . . 3 |
9 | 2 | wl 59 | . . . 4 |
10 | 9 | alval 132 | . . 3 |
11 | 8, 10 | a1i 28 | . 2 |
12 | 7, 11 | mpbir 77 | 1 |
Colors of variables: type var term |
Syntax hints: tv 1 hb 3 kc 5 kl 6 ke 7 kt 8 kbr 9 wffMMJ2 11 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 ax-eta 165 |
This theorem depends on definitions: df-ov 65 df-al 116 |
This theorem is referenced by: alimdv 172 alnex 174 isfree 176 ax5 194 ax7 196 |
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