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Theorem alrimdd 1516
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (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)
21nfrd 1429 . 2 (𝜑 → (𝜓 → ∀𝑥𝜓))
3 alrimdd.1 . . 3 𝑥𝜑
4 alrimdd.3 . . 3 (𝜑 → (𝜓𝜒))
53, 4alimd 1430 . 2 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
62, 5syld 44 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-5 1352  ax-gen 1354  ax-4 1416
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  alrimd  1517
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