Theorem exrot3 777

Description: Rotate existential quantifiers.

Assertion

Ref	Expression
exrot3	⊢ (∃x∃y∃zφ ↔ ∃y∃z∃xφ)

Proof of Theorem exrot3

Step	Hyp	Ref	Expression
1		excom13 776	. 2 ⊢ (∃x∃y∃zφ ↔ ∃z∃y∃xφ)
2		excom 728	. 2 ⊢ (∃z∃y∃xφ ↔ ∃y∃z∃xφ)
3	1, 2	bitr 151	1 ⊢ (∃x∃y∃zφ ↔ ∃y∃z∃xφ)

Syntax hints:   ↔ wb 127  ∃wex 678

This theorem is referenced by:  cbvop 2473  dmoprab 3031  rnoprab 3033  xpassen 3344  genpn0 3900  genpass 3906

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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