Theorem nfia1 1856

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 1788	. 2 ⊢ Ⅎx∀xφ
2		nfa1 1788	. 2 ⊢ Ⅎx∀xψ
3	1, 2	nfim 1813	1 ⊢ Ⅎx(∀xφ → ∀xψ)

Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)