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Theorem sylg 1804
Description: A syllogism combined with generalization. Inference associated with sylgt 1803. General form of alrimih 1805. (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 1793 . 2 (∀𝑥𝜓 → ∀𝑥𝜒)
41, 3syl 17 1 (𝜑 → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1520
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1777  ax-4 1791
This theorem is referenced by:  alrimih  1805  aev2  2039  ax9ALT  2791  ssrel  5543  kmlem1  9422  bnj1476  31735  bnj1533  31740  bj-ax12ig  33574  axc11n11  33618  bj-modalbe  33624  bj-modal4  33650  bj-19.12  33884  mpobi123f  34991  mptbi12f  34995
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