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Mirrors > Home > HOLE Home > Th. List > distrl | Unicode version |
Description: Distribution of lambda abstraction over substitution. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
distrl.1 |
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distrl.2 |
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Ref | Expression |
---|---|
distrl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | weq 41 |
. 2
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2 | distrl.1 |
. . . . 5
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3 | 2 | wl 66 |
. . . 4
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4 | 3 | wl 66 |
. . 3
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5 | distrl.2 |
. . 3
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6 | 4, 5 | wc 50 |
. 2
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7 | 2 | wl 66 |
. . . 4
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8 | 7, 5 | wc 50 |
. . 3
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9 | 8 | wl 66 |
. 2
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10 | 2, 5 | ax-distrl 70 |
. 2
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11 | 1, 6, 9, 10 | 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-wl 65 ax-distrl 70 ax-wov 71 |
This theorem depends on definitions: df-ov 73 |
This theorem is referenced by: hbl 112 ovl 117 |
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