Theorem nfaba1 2494

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.)

Assertion

Ref	Expression
nfaba1	⊢ Ⅎx{y ∣ ∀xφ}

Proof of Theorem nfaba1

Step	Hyp	Ref	Expression
1		nfa1 1788	. 2 ⊢ Ⅎx∀xφ
2	1	nfab 2493	1 ⊢ Ⅎx{y ∣ ∀xφ}

Syntax hints:  ∀wal 1540  {cab 2339  Ⅎwnfc 2476

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  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-nfc 2478

This theorem is referenced by:  nfiota1  4341  nfopd  4605  nfimad  4954  nffvd  5335