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Theorem sylg 1747
Description: A syllogism combined with generalization. Inference associated with sylgt 1746. General form of alrimih 1748. (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 1736 . 2 (∀𝑥𝜓 → ∀𝑥𝜒)
41, 3syl 17 1 (𝜑 → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1719  ax-4 1734
This theorem is referenced by:  alrimih  1748  aev2  1983  trint  4733  ssrel  5173  kmlem1  8924  bnj1476  30660  bnj1533  30665  bj-ax12ig  32292  axc11n11  32349  bj-modalbe  32355  bj-ax9-2  32573
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