Theorem mormo 3357

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 2553	. 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		df-rmo 3352	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	sylibr 234	1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∈ wcel 2114  ∃*wmo 2538  ∃*wrmo 3351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-mo 2540  df-rmo 3352

This theorem is referenced by:  reueq  3697  reusv1  5344  brdom4  10452  phpreu  37855