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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 149 | . 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 5893 onssneli 5981 tz7.48-2 7691 tz7.49 7694 php 8301 nndomo 8311 elirrv 8658 setind 8775 zorn2lem3 9523 alephval2 9597 inar1 9800 dfon2lem6 32030 sltres 32153 finminlem 32650 onint1 32786 poimirlem4 33747 gneispace 38959 |
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