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Mirrors > Home > MPE Home > Th. List > Mathboxes > prtlem60 | Structured version Visualization version GIF version |
Description: Lemma for prter3 36892. (Contributed by Rodolfo Medina, 9-Oct-2010.) |
Ref | Expression |
---|---|
prtlem60.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
prtlem60.2 | ⊢ (𝜓 → (𝜃 → 𝜏)) |
Ref | Expression |
---|---|
prtlem60 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prtlem60.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | prtlem60.2 | . . 3 ⊢ (𝜓 → (𝜃 → 𝜏)) | |
3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏))) |
4 | 1, 3 | syldd 72 | 1 ⊢ (𝜑 → (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: (None) |
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