Theorem moani 2256

Description: "At most one" is still true when a conjunct is added. (Contributed by NM, 9-Mar-1995.)

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 2255	. 2 ⊢ (∃*xφ → ∃*x(ψ ∧ φ))
3	1, 2	ax-mp 5	1 ⊢ ∃*x(ψ ∧ φ)

Syntax hints:   ∧ wa 358  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by:  euxfr2  3021  ovmpt2x  5712