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Mirrors > Home > HOLE Home > Th. List > 3eqtr4i | Unicode version |
Description: Transitivity of equality. (Contributed by Mario Carneiro, 7-Oct-2014.) |
Ref | Expression |
---|---|
3eqtr4i.1 |
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3eqtr4i.2 |
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3eqtr4i.3 |
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3eqtr4i.4 |
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Ref | Expression |
---|---|
3eqtr4i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr4i.1 |
. . 3
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2 | 3eqtr4i.3 |
. . 3
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3 | 1, 2 | eqtypri 81 |
. 2
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4 | 3eqtr4i.2 |
. . 3
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5 | 1, 4 | eqtypi 78 |
. . . . 5
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6 | 3eqtr4i.4 |
. . . . 5
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7 | 5, 6 | eqtypri 81 |
. . . 4
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8 | 7, 6 | eqcomi 79 |
. . 3
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9 | 1, 4, 8 | eqtri 95 |
. 2
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10 | 3, 2, 9 | eqtri 95 |
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 ax-eqtypri 80 |
This theorem depends on definitions: df-ov 73 |
This theorem is referenced by: 3eqtr3i 97 oveq123 98 hbxfrf 107 leqf 181 exnal 201 |
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