Theorem nfaba1 2756

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 2015	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfab 2755	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1473  {cab 2596  Ⅎwnfc 2738

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-nfc 2740

This theorem is referenced by:  nfopd  4357  nfimad  5394  nfiota1  5770  nffvd  6112  nfunidALT2  33274  nfunidALT  33275  nfopdALT  33276  setrec1  42237