Theorem nfra1 2665

Description: x is not free in ∀x ∈ Aφ. (Contributed by NM, 18-Oct-1996.) (Revised by Mario Carneiro, 7-Oct-2016.)

Assertion

Ref	Expression
nfra1	⊢ Ⅎx∀x ∈ A φ

Proof of Theorem nfra1

Step	Hyp	Ref	Expression
1		df-ral 2620	. 2 ⊢ (∀x ∈ A φ ↔ ∀x(x ∈ A → φ))
2		nfa1 1788	. 2 ⊢ Ⅎx∀x(x ∈ A → φ)
3	1, 2	nfxfr 1570	1 ⊢ Ⅎx∀x ∈ A φ

Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544   ∈ wcel 1710  ∀wral 2615

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-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-ral 2620

This theorem is referenced by:  nfra2  2669  r19.12  2728  ralbi  2751  ralcom2  2776  nfss  3267  ralidm  3654  nfii1  3999  dfiun2g  4000  ncfinraise  4482  fun11iun  5306  chfnrn  5400  ffnfv  5428  mpteq12f  5656  mpt2eq123  5662  fvmptss  5706