Theorem moanimv 1052

Description: Introduction of a conjunct into "at most one" quantifier.

Assertion

Ref	Expression
moanimv	⊢ (∃*x(φ ∧ ψ) ↔ (φ → ∃*xψ))

Distinct variable group(s):   φ,x

Proof of Theorem moanimv

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (φ → ∀xφ)
2	1	moanim 1051	1 ⊢ (∃*x(φ ∧ ψ) ↔ (φ → ∃*xψ))

Syntax hints:   → wi 2   ↔ wb 127   ∧ wa 196  ∃*wmo 1008

This theorem is referenced by:  euanv 1053  2reuswap 1341  funcnv 2703  funopabex 2742  zfrep6 2744  fnopabg 2745  fvopab3ig 2869  fnoprab 3038  oprabex 3044  oprabvalig 3048  th3qcor 3252

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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