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Axiom ax-coll 3863
 Description: Axiom of Collection. Axiom 7 of [Crosilla], p. "Axioms of CZF and IZF" (with unnecessary quantifier removed). It is similar to bnd 3916 but uses a freeness hypothesis in place of one of the distinct variable constraints. (Contributed by Jim Kingdon, 23-Aug-2018.)
Hypothesis
Ref Expression
ax-coll.1 𝑏φ
Assertion
Ref Expression
ax-coll (x 𝑎 yφ𝑏x 𝑎 y 𝑏 φ)
Distinct variable group:   x,y,𝑎,𝑏
Allowed substitution hints:   φ(x,y,𝑎,𝑏)

Detailed syntax breakdown of Axiom ax-coll
StepHypRef Expression
1 wph . . . 4 wff φ
2 vy . . . 4 setvar y
31, 2wex 1378 . . 3 wff yφ
4 vx . . 3 setvar x
5 va . . . 4 setvar 𝑎
65cv 1241 . . 3 class 𝑎
73, 4, 6wral 2300 . 2 wff x 𝑎 yφ
8 vb . . . . . 6 setvar 𝑏
98cv 1241 . . . . 5 class 𝑏
101, 2, 9wrex 2301 . . . 4 wff y 𝑏 φ
1110, 4, 6wral 2300 . . 3 wff x 𝑎 y 𝑏 φ
1211, 8wex 1378 . 2 wff 𝑏x 𝑎 y 𝑏 φ
137, 12wi 4 1 wff (x 𝑎 yφ𝑏x 𝑎 y 𝑏 φ)
 Colors of variables: wff set class This axiom is referenced by:  repizf  3864  bnd  3916
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