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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  F/ b
Assertion
Ref Expression
ax-coll  a  b  a  b
Distinct variable group:   ,, a, b
Allowed substitution hints:   (,, a, b)

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