Theorem nfaba1 2337

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 1551	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfab 2336	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1361  {cab 2174  Ⅎwnfc 2318

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773  df-clab 2175  df-nfc 2320

This theorem is referenced by:  nfopd  3809  nfimad  4993  nfiota1  5194  nffvd  5541