Theorem exdistr2 969

Description: Distribution of existential quantifiers.

Assertion

Ref	Expression
exdistr2	⊢ (∃x∃y∃z(φ ∧ ψ) ↔ ∃x(φ ∧ ∃y∃zψ))

Distinct variable group(s):   φ,y   φ,z

fTR ALIGN=LEFT>

Proof of Theorem exdistr2

Step	Hyp	Ref	Expression
1		19.42vv 968	. 2 ⊢ (∃y∃z(φ ∧ ψ) ↔ (φ ∧ ∃y∃zψ))
2	1	biex 733	1 ⊢ (∃x∃y∃z(φ ∧ ψ) ↔ ∃x(φ ∧ ∃y∃zψ))

Syntax hints:   ↔ wb 127   ∧ wa 196  ∃wex 678

This theorem is referenced by:  opabid 2099

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-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679

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