Theorem moexexv 1059

Description: "At most one" double quantification.

Assertion

Ref	Expression
moexexv	⊢ ((∃*xφ ∧ ∀x∃*yψ) → ∃*y∃x(φ ∧ ψ))

Distinct variable group(s):   φ,y

Proof of Theorem moexexv

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (φ → ∀yφ)
2	1	moexex 1058	1 ⊢ ((∃*xφ ∧ ∀x∃*yψ) → ∃*y∃x(φ ∧ ψ))

Syntax hints:   → wi 2   ∧ wa 196  ∀wal 672  ∃wex 678  ∃*wmo 1008

This theorem is referenced by:  mosub 1433  funco 2696

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  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010

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