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Theorem bnd 3899
Description: A very strong generalization of the Axiom of Replacement (compare zfrep6 3848). Its strength lies in the rather profound fact that φ(x, y) does not have to be a "function-like" wff, as it does in the standard Axiom of Replacement. This theorem is sometimes called the Boundedness Axiom. In the context of IZF, it is just a slight variation of ax-coll 3846. (Contributed by NM, 17-Oct-2004.)
Ref Expression
bnd (x z yφwx z y w φ)
Distinct variable groups:   φ,z,w   x,y,z,w
Allowed substitution hints:   φ(x,y)

Proof of Theorem bnd
StepHypRef Expression
1 nfv 1402 . 2 wφ
21ax-coll 3846 1 (x z yφwx z y w φ)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1362  wral 2284  wrex 2285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1318  ax-17 1400  ax-coll 3846
This theorem depends on definitions:  df-bi 110  df-nf 1330
This theorem is referenced by:  bnd2  3900
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