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Theorem alrimd 2071
 Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2062. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alrimd.1 𝑥𝜑
alrimd.2 𝑥𝜓
alrimd.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alrimd (𝜑 → (𝜓 → ∀𝑥𝜒))

Proof of Theorem alrimd
StepHypRef Expression
1 alrimd.1 . 2 𝑥𝜑
2 alrimd.2 . . 3 𝑥𝜓
32a1i 11 . 2 (𝜑 → Ⅎ𝑥𝜓)
4 alrimd.3 . 2 (𝜑 → (𝜓𝜒))
51, 3, 4alrimdd 2070 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473  Ⅎwnf 1699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701 This theorem is referenced by:  moexex  2529  ralrimd  2942  pssnn  8063  fiint  8122  wl-mo3t  32537  pm14.24  37655
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