Theorem nfreu1 2782

Description: x is not free in ∃!x ∈ Aφ. (Contributed by NM, 19-Mar-1997.)

Assertion

Ref	Expression
nfreu1	⊢ Ⅎx∃!x ∈ A φ

Proof of Theorem nfreu1

Step	Hyp	Ref	Expression
1		df-reu 2622	. 2 ⊢ (∃!x ∈ A φ ↔ ∃!x(x ∈ A ∧ φ))
2		nfeu1 2214	. 2 ⊢ Ⅎx∃!x(x ∈ A ∧ φ)
3	1, 2	nfxfr 1570	1 ⊢ Ⅎx∃!x ∈ A φ

Syntax hints:   ∧ wa 358  Ⅎwnf 1544   ∈ wcel 1710  ∃!weu 2204  ∃!wreu 2617

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

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-eu 2208  df-reu 2622

This theorem is referenced by: (None)