Theorem exrot3 2170

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 2169	. 2 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑)
2		excom 2167	. 2 ⊢ (∃𝑧∃𝑦∃𝑥𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)
3	1, 2	bitri 275	1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)

Syntax hints:   ↔ wb 206  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-11 2162

This theorem depends on definitions:  df-bi 207  df-ex 1781

This theorem is referenced by:  opabn0  5499  dmoprab  7459  rnoprab  7461  xpassen  8997  elima4  35919  brimg  36078  ellines  36295  rnxrn  38545  fundcmpsurinj  47597