HomeHome Metamath Proof Explorer < Previous   Next >
Related theorems
Unicode version

Theorem axreg 4574
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 4573 . 2 |- (E.x x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))
2119.23bi 1063 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 223  A.wal 952   e. wcel 956  E.wex 978
This theorem is referenced by:  zfregcl 4575  axregndlem2 4935
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 971  ax-reg 4573
This theorem depends on definitions:  df-bi 147  df-ex 979
Copyright terms: Public domain