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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)

Colors of variables: wff setvar class

Syntax hints: ↔ wb 176 ∃wex 1541

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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