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Axiom ax-setind 4204
Description: Axiom of -Induction (also known as set induction). An axiom of Intuitionistic Zermelo-Fraenkel set theory. Axiom 9 of [Crosilla] p. "Axioms of CZF and IZF". This replaces the Axiom of Foundation (also called Regularity) from Zermelo-Fraenkel set theory. (Contributed by Jim Kingdon, 19-Oct-2018.)
Assertion
Ref Expression
ax-setind  a  a  a  a
Distinct variable groups:   , a   ,
Allowed substitution hint:   ( a)

Detailed syntax breakdown of Axiom ax-setind
StepHypRef Expression
1 wph . . . . . 6
2 va . . . . . 6  setvar  a
3 vy . . . . . 6  setvar
41, 2, 3wsb 1627 . . . . 5  a
52cv 1227 . . . . 5  a
64, 3, 5wral 2284 . . . 4  a  a
76, 1wi 4 . . 3  a  a
87, 2wal 1226 . 2  a  a  a
91, 2wal 1226 . 2  a
108, 9wi 4 1  a  a  a  a
Colors of variables: wff set class
This axiom is referenced by:  setindel  4205  elirr  4208  en2lp  4216  tfi  4232  setindft  7183  setindis  7185
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