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Mirrors > Home > MPE Home > Th. List > syl6ci | Structured version Visualization version GIF version |
Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 18-Mar-2012.) |
Ref | Expression |
---|---|
syl6ci.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
syl6ci.2 | ⊢ (𝜑 → 𝜃) |
syl6ci.3 | ⊢ (𝜒 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
syl6ci | ⊢ (𝜑 → (𝜓 → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6ci.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | syl6ci.2 | . . 3 ⊢ (𝜑 → 𝜃) | |
3 | 2 | a1d 25 | . 2 ⊢ (𝜑 → (𝜓 → 𝜃)) |
4 | syl6ci.3 | . 2 ⊢ (𝜒 → (𝜃 → 𝜏)) | |
5 | 1, 3, 4 | syl6c 70 | 1 ⊢ (𝜑 → (𝜓 → 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: ordelord 5745 f1dmex 7136 omeulem2 7663 2pwuninel 8115 isumrpcl 14575 kqfvima 21533 caubl 23106 nbupgr 26240 nbumgrvtx 26242 umgr2adedgspth 26844 soseq 31751 btwnconn1lem12 32205 sbcim2g 38748 ee21an 38959 |
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