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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. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
eqtru.1 |
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Ref | Expression |
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eqtru |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtru.1 |
. . 3
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2 | wtru 43 |
. . 3
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3 | 1, 2 | adantr 55 |
. 2
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4 | 1 | ax-cb1 29 |
. . . 4
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5 | 1 | ax-cb2 30 |
. . . 4
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6 | 4, 5 | wct 48 |
. . 3
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7 | tru 44 |
. . 3
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8 | 6, 7 | a1i 28 |
. 2
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9 | 3, 8 | ded 84 |
1
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Colors of variables: type var term |
Syntax hints: ![]() ![]() ![]() ![]() |
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-weq 40 ax-refl 42 ax-eqmp 45 ax-ded 46 ax-wct 47 ax-wc 49 ax-ceq 51 ax-wov 71 |
This theorem depends on definitions: df-ov 73 |
This theorem is referenced by: hbth 109 alrimiv 151 dfan2 154 olc 164 orc 165 alrimi 182 exmid 199 ax9 212 |
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