Theorem exrot3 1704

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 1703	. 2 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑)
2		excom 1678	. 2 ⊢ (∃𝑧∃𝑦∃𝑥𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)
3	1, 2	bitri 184	1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑)

Syntax hints:   ↔ wb 105  ∃wex 1506

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-ial 1548

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  opabm  4316  rexiunxp  4809  dmoprab  6007  rnoprab  6009  cnvoprab  6301  xpassen  6898  dmaddpq  7463  dmmulpq  7464