Theorem exrot3 1626

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 1625	. 2 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑)
2		excom 1600	. 2 ⊢ (∃𝑧∃𝑦∃𝑥𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)
3	1, 2	bitri 183	1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)

Syntax hints:   ↔ wb 104  ∃wex 1427

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-ial 1473

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  opabm  4118  rexiunxp  4593  dmoprab  5745  rnoprab  5747  cnvoprab  6015  xpassen  6602  dmaddpq  7001  dmmulpq  7002