Theorem nfa2 1558

Description: Lemma 24 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.)

Assertion

Ref	Expression
nfa2	⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Proof of Theorem nfa2

Step	Hyp	Ref	Expression
1		nfa1 1521	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2	1	nfal 1555	1 ⊢ Ⅎ𝑥∀𝑦∀𝑥𝜑

Syntax hints:  ∀wal 1329  Ⅎwnf 1436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  cbv1h  1723  csbie2t  3043  copsex2t  4162  fnoprabg  5865  strcollnft  13171