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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee323 | Structured version Visualization version GIF version |
Description: e323 38014 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee323.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
ee323.2 | ⊢ (𝜑 → (𝜓 → 𝜏)) |
ee323.3 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) |
ee323.4 | ⊢ (𝜃 → (𝜏 → (𝜂 → 𝜁))) |
Ref | Expression |
---|---|
ee323 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜁))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee323.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | ee323.2 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜏)) | |
3 | 2 | a1dd 48 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
4 | ee323.3 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) | |
5 | ee323.4 | . 2 ⊢ (𝜃 → (𝜏 → (𝜂 → 𝜁))) | |
6 | 1, 3, 4, 5 | ee333 37734 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 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: e323 38014 trintALT 38139 |
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