Theorem nfia1 1633

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 1594	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		nfa1 1594	. 2 ⊢ Ⅎ𝑥∀𝑥𝜓
3	1, 2	nfim 1625	1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1400  Ⅎwnf 1513

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 1500  ax-gen 1502  ax-4 1563  ax-ial 1587  ax-i5r 1588

This theorem depends on definitions:  df-bi 117  df-nf 1514

This theorem is referenced by: (None)