Theorem moor 2581

Description: "At most one" is still the case when a disjunct is removed. (Contributed by NM, 5-Apr-2004.)

Assertion

Ref	Expression
moor	⊢ (∃*𝑥(𝜑 ∨ 𝜓) → ∃*𝑥𝜑)

Proof of Theorem moor

Step	Hyp	Ref	Expression
1		orc 880	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	moimi 2572	1 ⊢ (∃*𝑥(𝜑 ∨ 𝜓) → ∃*𝑥𝜑)

This proof depends on syntax axioms:   → wi 4   ∨ wo 860  ∃*wmo 2564

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1809  df-mo 2566

This theorem is used by:  mooran2  2583