Theorem nfia1 1518

Description: Lemma 23 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.)

Assertion

Ref	Expression
nfia1	⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓)

Proof of Theorem nfia1

Step	Hyp	Ref	Expression
1		nfa1 1480	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		nfa1 1480	. 2 ⊢ Ⅎ𝑥∀𝑥𝜓
3	1, 2	nfim 1510	1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1288  Ⅎwnf 1395

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-4 1446  ax-ial 1473  ax-i5r 1474

This theorem depends on definitions:  df-bi 116  df-nf 1396

This theorem is referenced by: (None)