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Theorem axreg 6037
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 6036 . 2 |- (E.x x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))
2119.23bi 1544 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 377  A.wal 1366  E.wex 1371   e. wcel 1451
This theorem is referenced by:  zfregcl 6038  axregndlem2 6598
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-4 1486  ax-reg 6036
This theorem depends on definitions:  df-bi 185  df-ex 1372
Copyright terms: Public domain