Theorem nfia1 2193

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 2191	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		nfa1 2191	. 2 ⊢ Ⅎ𝑥∀𝑥𝜓
3	1, 2	nfim 1931	1 ⊢ Ⅎ𝑥(∀𝑥𝜑 → ∀𝑥𝜓)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-10 2180

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817

This theorem is used by:  dfmoeu  2563  2eu6  2684  regsfromsetind  37504