Theorem moan 1046

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

Assertion

Ref	Expression
moan	⊢ (∃*xφ → ∃*x(ψ ∧ φ))

Proof of Theorem moan

Step	Hyp	Ref	Expression
1		immo 1043	. 2 ⊢ (∀x((ψ ∧ φ) → φ) → (∃*xφ → ∃*x(ψ ∧ φ)))
2		pm3.27 260	. 2 ⊢ ((ψ ∧ φ) → φ)
3	1, 2	mpg 684	1 ⊢ (∃*xφ → ∃*x(ψ ∧ φ))

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

This theorem is referenced by:  moani 1047  mooran1 1049  reuxfr2 1579  funin 2708

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

metamath.org