Theorem mormo 2677

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 2083	. 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
2		df-rmo 2452	. 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑))
3	1, 2	sylibr 133	1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑)

Syntax hints:   → wi 4   ∧ wa 103  ∃*wmo 2015   ∈ wcel 2136  ∃*wrmo 2447

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-eu 2017  df-mo 2018  df-rmo 2452

This theorem is referenced by:  reueq  2925  reusv1  4436