Theorem moor 2090

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 707	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2	1	moimi 2084	1 ⊢ (∃*𝑥(𝜑 ∨ 𝜓) → ∃*𝑥𝜑)

Syntax hints:   → wi 4   ∨ wo 703  ∃*wmo 2020

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-eu 2022  df-mo 2023

This theorem is referenced by:  mooran2  2092