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Theorem alrimih 1919
Description: Inference form of Theorem 19.21 of [Margaris] p. 90. See 19.21 2241 and 19.21h 2310. Instance of sylg 1918. (Contributed by NM, 9-Jan-1993.) (Revised by BJ, 31-Mar-2021.)
Hypotheses
Ref Expression
alrimih.1 (𝜑 → ∀𝑥𝜑)
alrimih.2 (𝜑𝜓)
Assertion
Ref Expression
alrimih (𝜑 → ∀𝑥𝜓)

Proof of Theorem alrimih
StepHypRef Expression
1 alrimih.1 . 2 (𝜑 → ∀𝑥𝜑)
2 alrimih.2 . 2 (𝜑𝜓)
31, 2sylg 1918 1 (𝜑 → ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1651
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1891  ax-4 1905
This theorem is referenced by:  nexdh  1963  albidh  1964  alrimiv  2023  ax12i  2063  cbvaliw  2105  nf5dh  2191  alrimi  2248  hbnd  2320  cbvalv  2412  eujustALT  2612  axi5r  2769  hbralrimi  3135  bnj1093  31565  bj-abv  33392  bj-ab0  33393  mpt2bi123f  34457  axc4i-o  34919  equidq  34945  aev-o  34952  ax12f  34961  axc5c4c711  39383  hbimpg  39540  gen11nv  39612
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