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Mirrors > Home > ILE Home > Th. List > ax-coll | Unicode version |
Description: Axiom of Collection. Axiom 7 of [Crosilla], p. "Axioms of CZF and IZF" (with unnecessary quantifier removed). It is similar to bnd 4174 but uses a freeness hypothesis in place of one of the distinct variable conditions. (Contributed by Jim Kingdon, 23-Aug-2018.) |
Ref | Expression |
---|---|
ax-coll.1 |
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Ref | Expression |
---|---|
ax-coll |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph |
. . . 4
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2 | vy |
. . . 4
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3 | 1, 2 | wex 1492 |
. . 3
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4 | vx |
. . 3
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5 | va |
. . . 4
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6 | 5 | cv 1352 |
. . 3
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7 | 3, 4, 6 | wral 2455 |
. 2
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8 | vb |
. . . . . 6
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9 | 8 | cv 1352 |
. . . . 5
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10 | 1, 2, 9 | wrex 2456 |
. . . 4
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11 | 10, 4, 6 | wral 2455 |
. . 3
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12 | 11, 8 | wex 1492 |
. 2
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13 | 7, 12 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: repizf 4121 bnd 4174 |
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