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Mirrors > Home > HOLE Home > Th. List > euval | Unicode version |
Description: Value of the 'exists unique' predicate. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
alval.1 |
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Ref | Expression |
---|---|
euval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | weu 141 |
. . 3
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2 | alval.1 |
. . 3
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3 | 1, 2 | wc 50 |
. 2
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4 | df-eu 133 |
. . 3
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5 | 1, 2, 4 | ceq1 89 |
. 2
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6 | wex 139 |
. . . 4
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7 | wal 134 |
. . . . . 6
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8 | wv 64 |
. . . . . . . . 9
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9 | wv 64 |
. . . . . . . . 9
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10 | 8, 9 | wc 50 |
. . . . . . . 8
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11 | wv 64 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 9, 11 | weqi 76 |
. . . . . . . 8
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13 | 10, 12 | weqi 76 |
. . . . . . 7
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14 | 13 | wl 66 |
. . . . . 6
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15 | 7, 14 | wc 50 |
. . . . 5
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16 | 15 | wl 66 |
. . . 4
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17 | 6, 16 | wc 50 |
. . 3
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18 | weq 41 |
. . . . . . . 8
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19 | 8, 2 | weqi 76 |
. . . . . . . . . 10
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20 | 19 | id 25 |
. . . . . . . . 9
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21 | 8, 9, 20 | ceq1 89 |
. . . . . . . 8
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22 | 18, 10, 12, 21 | oveq1 99 |
. . . . . . 7
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23 | 13, 22 | leq 91 |
. . . . . 6
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24 | 7, 14, 23 | ceq2 90 |
. . . . 5
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25 | 15, 24 | leq 91 |
. . . 4
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26 | 6, 16, 25 | ceq2 90 |
. . 3
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27 | 17, 2, 26 | cl 116 |
. 2
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28 | 3, 5, 27 | eqtri 95 |
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-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 |
This theorem depends on definitions: df-ov 73 df-al 126 df-an 128 df-im 129 df-ex 131 df-eu 133 |
This theorem is referenced by: (None) |
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