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Mirrors > Home > HOLE Home > Th. List > dedi | Unicode version |
Description: Deduction theorem for equality. (Contributed by Mario Carneiro, 7-Oct-2014.) |
Ref | Expression |
---|---|
dedi.1 |
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dedi.2 |
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Ref | Expression |
---|---|
dedi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dedi.1 |
. . 3
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2 | wtru 43 |
. . 3
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3 | 1, 2 | adantl 56 |
. 2
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4 | dedi.2 |
. . 3
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5 | 4, 2 | adantl 56 |
. 2
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6 | 3, 5 | 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-simpr 21 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-wctl 31 ax-wctr 32 ax-weq 40 ax-refl 42 ax-eqmp 45 ax-ded 46 ax-wc 49 ax-ceq 51 ax-wov 71 |
This theorem depends on definitions: df-ov 73 |
This theorem is referenced by: dfan2 154 notval2 159 alnex 186 notnot 200 |
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