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Theorem nfia1 2157
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 2155 . 2 𝑥𝑥𝜑
2 nfa1 2155 . 2 𝑥𝑥𝜓
31, 2nfim 1902 1 𝑥(∀𝑥𝜑 → ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540  wnf 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-10 2144
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-ex 1787  df-nf 1791
This theorem is referenced by:  dfmoeu  2536  2eu6  2659
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