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Theorem sylg 1814
Description: A syllogism combined with generalization. Inference associated with sylgt 1813. General form of alrimih 1815. (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 1803 . 2 (∀𝑥𝜓 → ∀𝑥𝜒)
41, 3syl 17 1 (𝜑 → ∀𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1787  ax-4 1801
This theorem is referenced by:  alrimih  1815  ax9ALT  2814  ssrel  5650  kmlem1  9564  bnj1476  32018  bnj1533  32023  bj-alrimd  33850  bj-exlimd  33855  bj-ax12ig  33866  axc11n11  33913  bj-modalbe  33919  bj-modal4  33945  bj-wnfanf  33950  bj-wnfenf  33951  bj-19.12  33987  mpobi123f  35321  mptbi12f  35325
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