Theorem mooran1 2258

Description: "At most one" imports disjunction to conjunction. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

Ref	Expression
mooran1	⊢ ((∃*xφ ∨ ∃*xψ) → ∃*x(φ ∧ ψ))

Proof of Theorem mooran1

Step	Hyp	Ref	Expression
1		simpl 443	. . 3 ⊢ ((φ ∧ ψ) → φ)
2	1	moimi 2251	. 2 ⊢ (∃*xφ → ∃*x(φ ∧ ψ))
3		moan 2255	. 2 ⊢ (∃*xψ → ∃*x(φ ∧ ψ))
4	2, 3	jaoi 368	1 ⊢ ((∃*xφ ∨ ∃*xψ) → ∃*x(φ ∧ ψ))

Syntax hints:   → wi 4   ∨ wo 357   ∧ 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: (None)