MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfia1 Structured version   Visualization version   GIF version

Theorem nfia1 2016
Description: Lemma 23 of [Monk2] p. 114. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nfia1 𝑥(∀𝑥𝜑 → ∀𝑥𝜓)

Proof of Theorem nfia1
StepHypRef Expression
1 nfa1 2014 . 2 𝑥𝑥𝜑
2 nfa1 2014 . 2 𝑥𝑥𝜓
31, 2nfim 1812 1 𝑥(∀𝑥𝜑 → ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1472  wnf 1698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-10 2005
This theorem depends on definitions:  df-bi 195  df-or 383  df-tru 1477  df-ex 1695  df-nf 1700
This theorem is referenced by:  mo2v  2464  2eu6  2545
  Copyright terms: Public domain W3C validator