Theorem nfaba1 2954

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 2195	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfab 2953	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1635  {cab 2792  Ⅎwnfc 2935

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-10 2185  ax-11 2201  ax-12 2214  ax-13 2420

This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2793  df-nfc 2937

This theorem is referenced by:  nfopd  4612  nfimad  5685  nfiota1  6062  nffvd  6416  nfunidALT2  34744  nfunidALT  34745  nfopdALT  34746  setrec1  43000