Theorem exrot4 1745

Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995.)

Assertion

Ref	Expression
exrot4	⊢ (∃x∃y∃z∃wφ ↔ ∃z∃w∃x∃yφ)

Proof of Theorem exrot4

Step	Hyp	Ref	Expression
1		excom13 1743	. . 3 ⊢ (∃y∃z∃wφ ↔ ∃w∃z∃yφ)
2	1	exbii 1582	. 2 ⊢ (∃x∃y∃z∃wφ ↔ ∃x∃w∃z∃yφ)
3		excom13 1743	. 2 ⊢ (∃x∃w∃z∃yφ ↔ ∃z∃w∃x∃yφ)
4	2, 3	bitri 240	1 ⊢ (∃x∃y∃z∃wφ ↔ ∃z∃w∃x∃yφ)

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:  sikexlem  4295  insklem  4304  elswap  4740  dfoprab2  5558  brpprod  5839  lecex  6115