Theorem moani 1047

Description: "At most one" is still true when a conjunct is added.

Hypothesis

Ref	Expression
moani.1	⊢ ∃*xφ

Assertion

Ref	Expression
moani	⊢ ∃*x(ψ ∧ φ)

Proof of Theorem moani

Step	Hyp	Ref	Expression
1		moani.1	. 2 ⊢ ∃*xφ
2		moan 1046	. 2 ⊢ (∃*xφ → ∃*x(ψ ∧ φ))
3	1, 2	ax-mp 6	1 ⊢ ∃*x(ψ ∧ φ)

Syntax hints:   ∧ wa 196  ∃*wmo 1008

This theorem is referenced by:  euxfr2 1435  reuxfr2 1579  fconst 2774  qsex 3231

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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