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Axiom ax-pr 3918
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 3852). (Contributed by NM, 14-Nov-2006.)
Assertion
Ref Expression
ax-pr
Distinct variable groups:   ,,   ,,

Detailed syntax breakdown of Axiom ax-pr
StepHypRef Expression
1 vw . . . . . 6  setvar
2 vx . . . . . 6  setvar
31, 2weq 1373 . . . . 5
4 vy . . . . . 6  setvar
51, 4weq 1373 . . . . 5
63, 5wo 616 . . . 4
7 vz . . . . 5  setvar
81, 7wel 1375 . . . 4
96, 8wi 4 . . 3
109, 1wal 1226 . 2
1110, 7wex 1362 1
Colors of variables: wff set class
This axiom is referenced by:  zfpair2  3919  bj-zfpair2  7133
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