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Mirrors > Home > MPE Home > Th. List > nsyli | Structured version Visualization version GIF version |
Description: A negated syllogism inference. (Contributed by NM, 3-May-1994.) |
Ref | Expression |
---|---|
nsyli.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
nsyli.2 | ⊢ (𝜃 → ¬ 𝜒) |
Ref | Expression |
---|---|
nsyli | ⊢ (𝜑 → (𝜃 → ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nsyli.2 | . 2 ⊢ (𝜃 → ¬ 𝜒) | |
2 | nsyli.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 2 | con3d 147 | . 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
4 | 1, 3 | syl5 33 | 1 ⊢ (𝜑 → (𝜃 → ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: necon3ad 2795 tz7.7 5666 onssneli 5754 tz7.48-2 7424 tz7.49 7427 php 8029 nndomo 8039 elirrv 8387 setind 8493 zorn2lem3 9203 alephval2 9273 inar1 9476 dfon2lem6 30937 sltres 31061 finminlem 31482 onint1 31618 poimirlem4 32583 gneispace 37452 |
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