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Mirrors > Home > HOLE Home > Th. List > distrc | Unicode version |
Description: Distribution of combination over substitution. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
distrc.1 |
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distrc.2 |
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distrc.3 |
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Ref | Expression |
---|---|
distrc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | weq 41 |
. 2
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2 | distrc.1 |
. . . . 5
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3 | distrc.2 |
. . . . 5
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4 | 2, 3 | wc 50 |
. . . 4
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5 | 4 | wl 66 |
. . 3
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6 | distrc.3 |
. . 3
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7 | 5, 6 | wc 50 |
. 2
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8 | 2 | wl 66 |
. . . 4
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9 | 8, 6 | wc 50 |
. . 3
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10 | 3 | wl 66 |
. . . 4
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11 | 10, 6 | wc 50 |
. . 3
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12 | 9, 11 | wc 50 |
. 2
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13 | 3, 6, 2 | ax-distrc 68 |
. 2
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14 | 1, 7, 12, 13 | 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-distrc 68 ax-wov 71 |
This theorem depends on definitions: df-ov 73 |
This theorem is referenced by: hbc 110 |
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