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Theorem nfia1 1518
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 1480 . 2 𝑥𝑥𝜑
2 nfa1 1480 . 2 𝑥𝑥𝜓
31, 2nfim 1510 1 𝑥(∀𝑥𝜑 → ∀𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1288  wnf 1395
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-4 1446  ax-ial 1473  ax-i5r 1474
This theorem depends on definitions:  df-bi 116  df-nf 1396
This theorem is referenced by: (None)
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