Theorem moor 2514

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 399	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	moimi 2508	1 ⊢ (∃*𝑥(𝜑 ∨ 𝜓) → ∃*𝑥𝜑)

Syntax hints:   → wi 4   ∨ wo 382  ∃*wmo 2459

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463

This theorem is referenced by:  mooran2  2516