Theorem nfnfc 2496

Description: Hypothesis builder for ℲyA. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfnfc.1	⊢ ℲxA

Assertion

Ref	Expression
nfnfc	⊢ ℲxℲyA

Proof of Theorem nfnfc

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-nfc 2479	. 2 ⊢ (ℲyA ↔ ∀zℲy z ∈ A)
2		nfnfc.1	. . . . 5 ⊢ ℲxA
3	2	nfcri 2484	. . . 4 ⊢ Ⅎx z ∈ A
4	3	nfnf 1845	. . 3 ⊢ ℲxℲy z ∈ A
5	4	nfal 1842	. 2 ⊢ Ⅎx∀zℲy z ∈ A
6	1, 5	nfxfr 1570	1 ⊢ ℲxℲyA

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  ax-12 1925  ax-ext 2334

This proof 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-cleq 2346  df-clel 2349  df-nfc 2479

This theorem is used by: (None)