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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee31 | Structured version Visualization version GIF version |
Description: e31 41893 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee31.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
ee31.2 | ⊢ (𝜑 → 𝜏) |
ee31.3 | ⊢ (𝜃 → (𝜏 → 𝜂)) |
Ref | Expression |
---|---|
ee31 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee31.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | ee31.2 | . . . 4 ⊢ (𝜑 → 𝜏) | |
3 | 2 | a1d 25 | . . 3 ⊢ (𝜑 → (𝜒 → 𝜏)) |
4 | 3 | a1d 25 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
5 | ee31.3 | . 2 ⊢ (𝜃 → (𝜏 → 𝜂)) | |
6 | 1, 4, 5 | ee33 41663 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) |
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: trintALT 42023 |
Copyright terms: Public domain | W3C validator |