Theorem mormo 3379

Description: Unrestricted "at most one" implies restricted "at most one". (Contributed by NM, 16-Jun-2017.)

Assertion

Ref	Expression
mormo	⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑)

Proof of Theorem mormo

Step	Hyp	Ref	Expression
1		moan 2544	. 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		df-rmo 3374	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	sylibr 233	1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑)

Syntax hints:   → wi 4   ∧ wa 394   ∈ wcel 2104  ∃*wmo 2530  ∃*wrmo 3373

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1780  df-mo 2532  df-rmo 3374

This theorem is referenced by:  reueq  3732  reusv1  5394  brdom4  10527  phpreu  36775