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Mirrors > Home > HOLE Home > Th. List > eta | Unicode version |
Description: The eta-axiom: a function is determined by its values. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
eta.1 |
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Ref | Expression |
---|---|
eta |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-eta 177 |
. 2
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2 | weq 41 |
. . . 4
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3 | wv 64 |
. . . . . 6
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4 | wv 64 |
. . . . . 6
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5 | 3, 4 | wc 50 |
. . . . 5
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6 | 5 | wl 66 |
. . . 4
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7 | 2, 6, 3 | wov 72 |
. . 3
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8 | eta.1 |
. . 3
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9 | 3, 8 | weqi 76 |
. . . . . . 7
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10 | 9 | id 25 |
. . . . . 6
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11 | 3, 4, 10 | ceq1 89 |
. . . . 5
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12 | 5, 11 | leq 91 |
. . . 4
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13 | 2, 6, 3, 12, 10 | oveq12 100 |
. . 3
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14 | 7, 8, 13 | cla4v 152 |
. 2
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15 | 1, 14 | syl 16 |
1
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Colors of variables: type var term |
Syntax hints: tv 1
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This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 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-wct 47 ax-wc 49 ax-ceq 51 ax-wv 63 ax-wl 65 ax-beta 67 ax-distrc 68 ax-leq 69 ax-wov 71 ax-eqtypi 77 ax-eqtypri 80 ax-hbl1 103 ax-17 105 ax-inst 113 ax-eta 177 |
This theorem depends on definitions: df-ov 73 df-al 126 |
This theorem is referenced by: cbvf 179 leqf 181 ax11 214 axext 219 |
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