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Theorem sylg 1825
Description: A syllogism combined with generalization. Inference associated with sylgt 1824. General form of alrimih 1826. (Contributed by BJ, 4-Oct-2019.)
Hypotheses
Ref Expression
sylg.1 (𝜑 → ∀𝑥𝜓)
sylg.2 (𝜓𝜒)
Assertion
Ref Expression
sylg (𝜑 → ∀𝑥𝜒)

Proof of Theorem sylg
StepHypRef Expression
1 sylg.1 . 2 (𝜑 → ∀𝑥𝜓)
2 sylg.2 . . 3 (𝜓𝜒)
32alimi 1814 . 2 (∀𝑥𝜓 → ∀𝑥𝜒)
41, 3syl 17 1 (𝜑 → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1798  ax-4 1812
This theorem is referenced by:  alrimih  1826  ax9ALT  2733  raleqbidvv  3338  csbied  3870  rzal  4439  ssrel  5693  ssrelOLD  5694  kmlem1  9906  bnj1476  32827  bnj1533  32832  bj-alrimd  34801  bj-exlimd  34806  bj-ax12ig  34817  axc11n11  34864  bj-modalbe  34870  bj-modal4  34896  bj-wnfanf  34901  bj-wnfenf  34902  bj-19.12  34943  bj-pm11.53vw  34958  mpobi123f  36320  mptbi12f  36324  ismnushort  41919
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