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Theorem alrimdd 2230
Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2222. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alrimdd.1 𝑥𝜑
alrimdd.2 (𝜑 → Ⅎ𝑥𝜓)
alrimdd.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alrimdd (𝜑 → (𝜓 → ∀𝑥𝜒))

Proof of Theorem alrimdd
StepHypRef Expression
1 alrimdd.2 . . 3 (𝜑 → Ⅎ𝑥𝜓)
21nf5rd 2213 . 2 (𝜑 → (𝜓 → ∀𝑥𝜓))
3 alrimdd.1 . . 3 𝑥𝜑
4 alrimdd.3 . . 3 (𝜑 → (𝜓𝜒))
53, 4alimd 2228 . 2 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
62, 5syld 47 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1630  wnf 1857
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-12 2196
This theorem depends on definitions:  df-bi 197  df-ex 1854  df-nf 1859
This theorem is referenced by:  alrimd  2231  wl-euequ1f  33669
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