Theorem nfaba1OLD 2917

Description: Obsolete version of nfaba1 2916 as of 14-May-2025. (Contributed by Mario Carneiro, 14-Oct-2016.) (Revised by GG, 20-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nfaba1OLD	⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfaba1OLD

Step	Hyp	Ref	Expression
1		nfa1 2152	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfab 2914	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1535  {cab 2717  Ⅎwnfc 2893

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2158  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-or 847  df-ex 1778  df-nf 1782  df-sb 2065  df-clab 2718  df-nfc 2895

This theorem is referenced by: (None)