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Mirrors > Home > HOLE Home > Th. List > eqtru | Unicode version |
Description: If a statement is provable, then it is equivalent to truth. |
Ref | Expression |
---|---|
eqtru.1 |
Ref | Expression |
---|---|
eqtru |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtru.1 | . . 3 | |
2 | wtru 40 | . . 3 | |
3 | 1, 2 | adantr 50 | . 2 |
4 | 1 | ax-cb1 29 | . . . 4 |
5 | 1 | ax-cb2 30 | . . . 4 |
6 | 4, 5 | wct 44 | . . 3 |
7 | tru 41 | . . 3 | |
8 | 6, 7 | a1i 28 | . 2 |
9 | 3, 8 | ded 74 | 1 |
Colors of variables: type var term |
Syntax hints: ke 7 kt 8 kbr 9 kct 10 wffMMJ2 11 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: hbth 99 alrimiv 141 dfan2 144 olc 154 orc 155 alrimi 170 exmid 186 ax9 199 |
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