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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee123 | Structured version Visualization version GIF version |
Description: e123 38010 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee123.1 | ⊢ (𝜑 → 𝜓) |
ee123.2 | ⊢ (𝜑 → (𝜒 → 𝜃)) |
ee123.3 | ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜂))) |
ee123.4 | ⊢ (𝜓 → (𝜃 → (𝜂 → 𝜁))) |
Ref | Expression |
---|---|
ee123 | ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜁))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee123.1 | . . . 4 ⊢ (𝜑 → 𝜓) | |
2 | 1 | a1d 25 | . . 3 ⊢ (𝜑 → (𝜏 → 𝜓)) |
3 | 2 | a1d 25 | . 2 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜓))) |
4 | ee123.2 | . . 3 ⊢ (𝜑 → (𝜒 → 𝜃)) | |
5 | 4 | a1dd 48 | . 2 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜃))) |
6 | ee123.3 | . 2 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜂))) | |
7 | ee123.4 | . 2 ⊢ (𝜓 → (𝜃 → (𝜂 → 𝜁))) | |
8 | 3, 5, 6, 7 | ee333 37734 | 1 ⊢ (𝜑 → (𝜒 → (𝜏 → 𝜁))) |
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 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 df-3an 1033 |
This theorem is referenced by: (None) |
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