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Mirrors > Home > HOLE Home > Th. List > ceq12 | Unicode version |
Description: Equality theorem for combination. (Contributed by Mario Carneiro, 7-Oct-2014.) |
Ref | Expression |
---|---|
ceq12.1 |
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ceq12.2 |
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ceq12.3 |
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ceq12.4 |
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Ref | Expression |
---|---|
ceq12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | weq 41 |
. 2
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2 | ceq12.1 |
. . 3
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3 | ceq12.2 |
. . 3
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4 | 2, 3 | wc 50 |
. 2
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5 | ceq12.3 |
. . . 4
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6 | 2, 5 | eqtypi 78 |
. . 3
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7 | ceq12.4 |
. . . 4
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8 | 3, 7 | eqtypi 78 |
. . 3
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9 | 6, 8 | wc 50 |
. 2
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10 | weq 41 |
. . . 4
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11 | 10, 2, 6, 5 | dfov1 74 |
. . 3
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12 | weq 41 |
. . . 4
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13 | 12, 3, 8, 7 | dfov1 74 |
. . 3
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14 | 2, 6, 3, 8 | ax-ceq 51 |
. . 3
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15 | 11, 13, 14 | syl2anc 19 |
. 2
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16 | 1, 4, 9, 15 | dfov2 75 |
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-trud 26 ax-cb1 29 ax-cb2 30 ax-weq 40 ax-refl 42 ax-eqmp 45 ax-wc 49 ax-ceq 51 ax-wov 71 ax-eqtypi 77 |
This theorem depends on definitions: df-ov 73 |
This theorem is referenced by: ceq1 89 ceq2 90 oveq123 98 hbc 110 ac 197 |
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