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Mirrors > Home > ILE Home > Th. List > ax-pr | Unicode version |
Description: The Axiom of Pairing of IZF set theory. Axiom 2 of [Crosilla] p. "Axioms of CZF and IZF", except (a) unnecessary quantifiers are removed, and (b) Crosilla has a biconditional rather than an implication (but the two are equivalent by bm1.3ii 4121). (Contributed by NM, 14-Nov-2006.) |
Ref | Expression |
---|---|
ax-pr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vw |
. . . . . 6
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2 | vx |
. . . . . 6
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3 | 1, 2 | weq 1503 |
. . . . 5
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4 | vy |
. . . . . 6
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5 | 1, 4 | weq 1503 |
. . . . 5
![]() ![]() ![]() ![]() |
6 | 3, 5 | wo 708 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | vz |
. . . . 5
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8 | 1, 7 | wel 2149 |
. . . 4
![]() ![]() ![]() ![]() |
9 | 6, 8 | wi 4 |
. . 3
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10 | 9, 1 | wal 1351 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 10, 7 | wex 1492 |
1
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Colors of variables: wff set class |
This axiom is referenced by: zfpair2 4207 bj-zfpair2 14318 |
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