Theorem axreg 4581

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

Step	Hyp	Ref	Expression
1		ax-reg 4580	. 2 |- (E.x x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))
2	1	19.23bi 1064	1 |- (x e. y -> E.x(x e. y /\ A.z(z e. x -> -. z e. y)))

Syntax hints:  -. wn 2   -> wi 3   /\ wa 223  A.wal 953   e. wcel 957  E.wex 979

This theorem is referenced by:  zfregcl 4582  axregndlem2 4942

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 972  ax-reg 4580

This theorem depends on definitions:  df-bi 147  df-ex 980

Copyright terms: Public domain