Theorem exrot3 1744

Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)

Assertion

Ref	Expression
exrot3	⊢ (∃x∃y∃zφ ↔ ∃y∃z∃xφ)

Proof of Theorem exrot3

Step	Hyp	Ref	Expression
1		excom13 1743	. 2 ⊢ (∃x∃y∃zφ ↔ ∃z∃y∃xφ)
2		excom 1741	. 2 ⊢ (∃z∃y∃xφ ↔ ∃y∃z∃xφ)
3	1, 2	bitri 240	1 ⊢ (∃x∃y∃zφ ↔ ∃y∃z∃xφ)

Syntax hints:   ↔ wb 176  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  dfpw12  4302  insklem  4305  opabn0  4717  setconslem4  4735  setconslem6  4737  dmoprab  5575  rnoprab  5577  dmtxp  5803  dmpprod  5841