Theorem nfnfc1 2493

Description: x is bound in ℲxA. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfnfc1	⊢ ℲxℲxA

Proof of Theorem nfnfc1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-nfc 2479	. 2 ⊢ (ℲxA ↔ ∀yℲx y ∈ A)
2		nfnf1 1790	. . 3 ⊢ ℲxℲx y ∈ A
3	2	nfal 1842	. 2 ⊢ Ⅎx∀yℲx y ∈ A
4	1, 3	nfxfr 1570	1 ⊢ ℲxℲxA

This proof depends on syntax axioms:  ∀wal 1540  Ⅎwnf 1544   ∈ wcel 1710  Ⅎwnfc 2477

This proof depends on 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 proof depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-nfc 2479

This theorem is used by:  vtoclgft  2906  sbcralt  3119  sbcrext  3120  csbiebt  3173  nfopd  4606  nfimad  4955  nffvd  5336