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Theorem sylg 1824
 Description: A syllogism combined with generalization. Inference associated with sylgt 1823. General form of alrimih 1825. (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 1813 . 2 (∀𝑥𝜓 → ∀𝑥𝜒)
41, 3syl 17 1 (𝜑 → ∀𝑥𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1797  ax-4 1811 This theorem is referenced by:  alrimih  1825  ax9ALT  2753  rzal  4401  ssrel  5626  kmlem1  9610  bnj1476  32347  bnj1533  32352  bj-alrimd  34347  bj-exlimd  34352  bj-ax12ig  34363  axc11n11  34410  bj-modalbe  34416  bj-modal4  34442  bj-wnfanf  34447  bj-wnfenf  34448  bj-19.12  34486  mpobi123f  35880  mptbi12f  35884
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