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Theorem alimdh 1372
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 4-Jan-2002.)
Hypotheses
Ref Expression
alimdh.1 (𝜑 → ∀𝑥𝜑)
alimdh.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alimdh (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Proof of Theorem alimdh
StepHypRef Expression
1 alimdh.1 . 2 (𝜑 → ∀𝑥𝜑)
2 alimdh.2 . . 3 (𝜑 → (𝜓𝜒))
32al2imi 1363 . 2 (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
41, 3syl 14 1 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1352  ax-gen 1354
This theorem is referenced by:  alrimdh  1384  hbald  1396  alimd  1430  hbimd  1481  dral1  1634  sbiedh  1686  ax16  1710  ax16i  1754  alimdv  1775
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