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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 1865. General form of alrimih 1867. (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 1855 | . 2 ⊢ (∀𝑥𝜓 → ∀𝑥𝜒) |
4 | 1, 3 | syl 17 | 1 ⊢ (𝜑 → ∀𝑥𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1599 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-gen 1839 ax-4 1853 |
This theorem is referenced by: alrimih 1867 aev2 2105 trintOLD 5004 ssrel 5455 kmlem1 9307 bnj1476 31516 bnj1533 31521 bj-ax12ig 33194 axc11n11 33261 bj-modalbe 33267 bj-ax9-2 33462 |
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