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Mirrors > Home > MPE Home > Th. List > sylg | Structured version Visualization version GIF version |
Description: A syllogism combined with generalization. Inference associated with sylgt 1824. General form of alrimih 1826. (Contributed by BJ, 4-Oct-2019.) |
Ref | Expression |
---|---|
sylg.1 | ⊢ (𝜑 → ∀𝑥𝜓) |
sylg.2 | ⊢ (𝜓 → 𝜒) |
Ref | Expression |
---|---|
sylg | ⊢ (𝜑 → ∀𝑥𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylg.1 | . 2 ⊢ (𝜑 → ∀𝑥𝜓) | |
2 | sylg.2 | . . 3 ⊢ (𝜓 → 𝜒) | |
3 | 2 | alimi 1814 | . 2 ⊢ (∀𝑥𝜓 → ∀𝑥𝜒) |
4 | 1, 3 | syl 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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