Theorem exdistr 1311

Description: Distribution of existential quantifiers.

Assertion

Ref	Expression
exdistr	⊢ (∃x∃y(φ ⋀ ψ) ↔ ∃x(φ ⋀ ∃yψ))

Distinct variable group:   φ,y

Proof of Theorem exdistr

Step	Hyp	Ref	Expression
1		19.42v 1310	. 2 ⊢ (∃y(φ ⋀ ψ) ↔ (φ ⋀ ∃yψ))
2	1	exbii 1053	1 ⊢ (∃x∃y(φ ⋀ ψ) ↔ ∃x(φ ⋀ ∃yψ))

Syntax hints:   ↔ wb 146   ⋀ wa 223  ∃wex 982

This theorem is referenced by:  19.42vv 1312  eeanv 1325  sbel2x 1347  reeanv 1781  sbccomglem 1991  iunn0 2612  uniuni 2886  imaiun 3870

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983

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