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Theorem alrimdh 1865
Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2208 and 19.21h 2296. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Hypotheses
Ref Expression
alrimdh.1 (𝜑 → ∀𝑥𝜑)
alrimdh.2 (𝜓 → ∀𝑥𝜓)
alrimdh.3 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
alrimdh (𝜑 → (𝜓 → ∀𝑥𝜒))

Proof of Theorem alrimdh
StepHypRef Expression
1 alrimdh.2 . 2 (𝜓 → ∀𝑥𝜓)
2 alrimdh.1 . . 3 (𝜑 → ∀𝑥𝜑)
3 alrimdh.3 . . 3 (𝜑 → (𝜓𝜒))
42, 3alimdh 1819 . 2 (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
51, 4syl5 34 1 (𝜑 → (𝜓 → ∀𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1797  ax-4 1811
This theorem is referenced by:  alrimdv  1931  ax12indn  36117  gen21nv  41109
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