Theorem nfre1 2671

Description: x is not free in ∃x ∈ Aφ. (Contributed by NM, 19-Mar-1997.) (Revised by Mario Carneiro, 7-Oct-2016.)

Assertion

Ref	Expression
nfre1	⊢ Ⅎx∃x ∈ A φ

Proof of Theorem nfre1

Step	Hyp	Ref	Expression
1		df-rex 2621	. 2 ⊢ (∃x ∈ A φ ↔ ∃x(x ∈ A ∧ φ))
2		nfe1 1732	. 2 ⊢ Ⅎx∃x(x ∈ A ∧ φ)
3	1, 2	nfxfr 1570	1 ⊢ Ⅎx∃x ∈ A φ

Syntax hints:   ∧ wa 358  ∃wex 1541  Ⅎwnf 1544   ∈ wcel 1710  ∃wrex 2616

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-6 1729

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-rex 2621

This theorem is referenced by:  2rmorex  3041  nfiu1  3998  fun11iun  5306