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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee03 | Structured version Visualization version GIF version |
Description: e03 41920 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee03.1 | ⊢ 𝜑 |
ee03.2 | ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏))) |
ee03.3 | ⊢ (𝜑 → (𝜏 → 𝜂)) |
Ref | Expression |
---|---|
ee03 | ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜂))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee03.1 | . . . . 5 ⊢ 𝜑 | |
2 | 1 | a1i 11 | . . . 4 ⊢ (𝜓 → 𝜑) |
3 | 2 | a1d 25 | . . 3 ⊢ (𝜓 → (𝜒 → 𝜑)) |
4 | 3 | a1dd 50 | . 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜑))) |
5 | ee03.2 | . 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏))) | |
6 | ee03.3 | . 2 ⊢ (𝜑 → (𝜏 → 𝜂)) | |
7 | 4, 5, 6 | ee33 41701 | 1 ⊢ (𝜓 → (𝜒 → (𝜃 → 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: ee03an 41923 suctrALT2 42017 |
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