Theorem exrot3 2045

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 2044	. 2 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑)
2		excom 2042	. 2 ⊢ (∃𝑧∃𝑦∃𝑥𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)
3	1, 2	bitri 264	1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)

Syntax hints:   ↔ wb 196  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-11 2034

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  opabn0  5006  dmoprab  6741  rnoprab  6743  xpassen  8054  cnvoprab  29498  elima4  31679  brimg  32044  ellines  32259