Theorem nfaba1OLD 2914

Description: Obsolete version of nfaba1 2913 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 2151	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfab 2911	1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑}

Syntax hints:  ∀wal 1538  {cab 2714  Ⅎwnfc 2890

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2157  ax-12 2177

This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-nfc 2892

This theorem is referenced by: (None)