Theorem mormo 2824

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 2255	. 2 ⊢ (∃*xφ → ∃*x(x ∈ A ∧ φ))
2		df-rmo 2623	. 2 ⊢ (∃*x ∈ A φ ↔ ∃*x(x ∈ A ∧ φ))
3	1, 2	sylibr 203	1 ⊢ (∃*xφ → ∃*x ∈ A φ)

Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∃*wmo 2205  ∃*wrmo 2618

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-rmo 2623

This theorem is referenced by:  reueq  3034