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Theorem axreg 5999
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 5998 . 2 |- (E.x x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))
2119.23bi 1551 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 3   -> wi 4   /\ wa 382  A.wal 1375  E.wex 1380   e. wcel 1459
This theorem is referenced by:  zfregcl 6000  axregndlem2 6569
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-4 1494  ax-reg 5998
This theorem depends on definitions:  df-bi 190  df-ex 1381
Copyright terms: Public domain