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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 152 | . 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
4 | 1, 3 | syl5 34 | 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 2956 tz7.7 6292 onssneli 6376 tz7.48-2 8273 tz7.49 8276 php 8993 phpOLD 9005 nndomogOLD 9009 elirrv 9355 setind 9492 zorn2lem3 10254 alephval2 10328 inar1 10531 dfon2lem6 33764 sltres 33865 finminlem 34507 onint1 34638 poimirlem4 35781 gneispace 41744 |
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