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Mirrors > Home > ILE Home > Th. List > syli | GIF version |
Description: Syllogism inference with common nested antecedent. (Contributed by NM, 4-Nov-2004.) |
Ref | Expression |
---|---|
syli.1 | ⊢ (𝜓 → (𝜑 → 𝜒)) |
syli.2 | ⊢ (𝜒 → (𝜑 → 𝜃)) |
Ref | Expression |
---|---|
syli | ⊢ (𝜓 → (𝜑 → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syli.1 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) | |
2 | syli.2 | . . 3 ⊢ (𝜒 → (𝜑 → 𝜃)) | |
3 | 2 | com12 27 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) |
4 | 1, 3 | sylcom 25 | 1 ⊢ (𝜓 → (𝜑 → 𝜃)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: ibd 167 bijadc 776 sbi2v 1772 elab3gf 2692 elreldm 4560 tz6.12c 5203 rntpos 5872 smores 5907 f1domg 6238 negm 8550 |
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