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Mirrors > Home > MPE Home > Th. List > mpsylsyld | Structured version Visualization version GIF version |
Description: Modus ponens combined with a double syllogism inference. (Contributed by Alan Sare, 22-Jul-2012.) |
Ref | Expression |
---|---|
mpsylsyld.1 | ⊢ 𝜑 |
mpsylsyld.2 | ⊢ (𝜓 → (𝜒 → 𝜃)) |
mpsylsyld.3 | ⊢ (𝜑 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
mpsylsyld | ⊢ (𝜓 → (𝜒 → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpsylsyld.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜓 → 𝜑) |
3 | mpsylsyld.2 | . 2 ⊢ (𝜓 → (𝜒 → 𝜃)) | |
4 | mpsylsyld.3 | . 2 ⊢ (𝜑 → (𝜃 → 𝜏)) | |
5 | 2, 3, 4 | sylsyld 59 | 1 ⊢ (𝜓 → (𝜒 → 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: vk15.4j 37755 onfrALTlem3 37780 ee02an 37945 |
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