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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: mtord 876 reu6 3717 axprlem3 5318 ordelord 6208 f1dmex 7652 omeulem2 8203 2pwuninel 8666 isumrpcl 15192 kqfvima 22332 caubl 23905 nbupgr 27120 nbumgrvtx 27122 umgr2adedgspth 27721 soseq 33091 btwnconn1lem12 33554 sbcim2g 40865 ee21an 41059 |
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