Theorem nfia1 1590

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 1551	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		nfa1 1551	. 2 ⊢ Ⅎ𝑥∀𝑥𝜓
3	1, 2	nfim 1582	1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1361  Ⅎwnf 1470

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-5 1457  ax-gen 1459  ax-4 1520  ax-ial 1544  ax-i5r 1545

This theorem depends on definitions:  df-bi 117  df-nf 1471

This theorem is referenced by: (None)