Theorem moor 2554

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 863	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	moimi 2545	1 ⊢ (∃*𝑥(𝜑 ∨ 𝜓) → ∃*𝑥𝜑)

Syntax hints:   → wi 4   ∨ wo 843  ∃*wmo 2538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813

This theorem depends on definitions:  df-bi 206  df-or 844  df-ex 1784  df-mo 2540

This theorem is referenced by:  mooran2  2556