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Theorem bnd 3916
Description: A very strong generalization of the Axiom of Replacement (compare zfrep6 3865). Its strength lies in the rather profound fact that  , 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 3863. (Contributed by NM, 17-Oct-2004.)
Ref Expression
Distinct variable groups:   ,,   ,,,
Allowed substitution hints:   (,)

Proof of Theorem bnd
StepHypRef Expression
1 nfv 1418 . 2  F/
21ax-coll 3863 1
Colors of variables: wff set class
Syntax hints:   wi 4  wex 1378  wral 2300  wrex 2301
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 1335  ax-17 1416  ax-coll 3863
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  bnd2  3917
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