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Theorem alrimd 2248
Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2239. (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 2247 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650  wnf 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-ex 1875  df-nf 1879
This theorem is referenced by:  moexex  2662  ralrimd  3105  pssnn  8384  fiint  8443  wl-mo3t  33715  pm14.24  39238
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