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Theorem axreg 6103
Description: Axiom of Regularity expressed more compactly.
Assertion
Ref Expression
axreg |- (x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))
Distinct variable group:   x,y,z

Proof of Theorem axreg
StepHypRef Expression
1 ax-reg 6102 . 2 |- (E.x x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))
2119.23bi 1683 1 |- (x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))
Colors of variables: wff set class
Syntax hints:  -. wn 2   -> wi 3   /\ wa 418  A.wal 1515  E.wex 1520   e. wcel 1594
This theorem is referenced by:  zfregcl 6104  axregndlem2 6816
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 1626  ax-reg 6102
This theorem depends on definitions:  df-bi 210  df-ex 1521
Copyright terms: Public domain