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Theorem hbia1 1532
Description: Lemma 23 of [Monk2] p. 114. (Contributed by NM, 29-May-2008.)
Assertion
Ref Expression
hbia1 ((∀𝑥𝜑 → ∀𝑥𝜓) → ∀𝑥(∀𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem hbia1
StepHypRef Expression
1 hba1 1521 . 2 (∀𝑥𝜑 → ∀𝑥𝑥𝜑)
2 hba1 1521 . 2 (∀𝑥𝜓 → ∀𝑥𝑥𝜓)
31, 2hbim 1525 1 ((∀𝑥𝜑 → ∀𝑥𝜓) → ∀𝑥(∀𝑥𝜑 → ∀𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1330
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1424  ax-gen 1426  ax-4 1488  ax-ial 1515  ax-i5r 1516
This theorem is referenced by: (None)
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