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Mirrors > Home > HOLE Home > Th. List > leqf | Unicode version |
Description: Equality theorem for lambda abstraction, using bound variable instead of distinct variables. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
leqf.1 |
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leqf.2 |
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leqf.3 |
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Ref | Expression |
---|---|
leqf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leqf.1 |
. . . . 5
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2 | 1 | wl 66 |
. . . 4
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3 | wv 64 |
. . . 4
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4 | 2, 3 | wc 50 |
. . 3
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5 | 4 | wl 66 |
. 2
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6 | leqf.2 |
. . . . 5
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7 | 6 | ax-cb1 29 |
. . . . . 6
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8 | 1 | beta 92 |
. . . . . 6
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9 | 7, 8 | a1i 28 |
. . . . 5
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10 | 1, 6 | eqtypi 78 |
. . . . . . 7
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11 | 10 | beta 92 |
. . . . . 6
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12 | 7, 11 | a1i 28 |
. . . . 5
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13 | 1, 6, 9, 12 | 3eqtr4i 96 |
. . . 4
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14 | weq 41 |
. . . . 5
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15 | wv 64 |
. . . . 5
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16 | 10 | wl 66 |
. . . . . 6
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17 | 16, 3 | wc 50 |
. . . . 5
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18 | 14, 15 | ax-17 105 |
. . . . 5
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19 | 1, 15 | ax-hbl1 103 |
. . . . . 6
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20 | 3, 15 | ax-17 105 |
. . . . . 6
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21 | 2, 3, 15, 19, 20 | hbc 110 |
. . . . 5
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22 | 10, 15 | ax-hbl1 103 |
. . . . . 6
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23 | 16, 3, 15, 22, 20 | hbc 110 |
. . . . 5
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24 | 14, 4, 15, 17, 18, 21, 23 | hbov 111 |
. . . 4
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25 | leqf.3 |
. . . 4
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26 | wv 64 |
. . . . . 6
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27 | 2, 26 | wc 50 |
. . . . 5
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28 | 16, 26 | wc 50 |
. . . . 5
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29 | 26, 3 | weqi 76 |
. . . . . . 7
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30 | 29 | id 25 |
. . . . . 6
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31 | 2, 26, 30 | ceq2 90 |
. . . . 5
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32 | 16, 26, 30 | ceq2 90 |
. . . . 5
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33 | 14, 27, 28, 31, 32 | oveq12 100 |
. . . 4
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34 | 29, 7 | eqid 83 |
. . . 4
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35 | 13, 24, 25, 33, 34 | ax-inst 113 |
. . 3
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36 | 4, 35 | leq 91 |
. 2
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37 | 2 | eta 178 |
. . 3
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38 | 7, 37 | a1i 28 |
. 2
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39 | 16 | eta 178 |
. . 3
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40 | 7, 39 | a1i 28 |
. 2
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41 | 5, 36, 38, 40 | 3eqtr3i 97 |
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: alrimi 182 axext 219 axrep 220 |
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