Theorem mooran2 2259

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

Assertion

Ref	Expression
mooran2	⊢ (∃*x(φ ∨ ψ) → (∃*xφ ∧ ∃*xψ))

Proof of Theorem mooran2

Step	Hyp	Ref	Expression
1		moor 2257	. 2 ⊢ (∃*x(φ ∨ ψ) → ∃*xφ)
2		olc 373	. . 3 ⊢ (ψ → (φ ∨ ψ))
3	2	moimi 2251	. 2 ⊢ (∃*x(φ ∨ ψ) → ∃*xψ)
4	1, 3	jca 518	1 ⊢ (∃*x(φ ∨ ψ) → (∃*xφ ∧ ∃*xψ))

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)