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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee212 | Structured version Visualization version GIF version |
Description: e212 37897 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee212.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
ee212.2 | ⊢ (𝜑 → 𝜃) |
ee212.3 | ⊢ (𝜑 → (𝜓 → 𝜏)) |
ee212.4 | ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂))) |
Ref | Expression |
---|---|
ee212 | ⊢ (𝜑 → (𝜓 → 𝜂)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee212.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | ee212.2 | . . 3 ⊢ (𝜑 → 𝜃) | |
3 | 2 | a1d 25 | . 2 ⊢ (𝜑 → (𝜓 → 𝜃)) |
4 | ee212.3 | . 2 ⊢ (𝜑 → (𝜓 → 𝜏)) | |
5 | ee212.4 | . 2 ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂))) | |
6 | 1, 3, 4, 5 | ee222 37729 | 1 ⊢ (𝜑 → (𝜓 → 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 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 |
This theorem is referenced by: (None) |
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