Theorem nfia1 2187

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 2185	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		nfa1 2185	. 2 ⊢ Ⅎ𝑥∀𝑥𝜓
3	1, 2	nfim 1925	1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567  Ⅎwnf 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-10 2175

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1809  df-nf 1813

This theorem is used by:  dfmoeu  2562  2eu6  2683  regsfromsetind  37078