![]() |
Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > ee112 | Structured version Visualization version GIF version |
Description: e112 37900 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee112.1 | ⊢ (𝜑 → 𝜓) |
ee112.2 | ⊢ (𝜑 → 𝜒) |
ee112.3 | ⊢ (𝜑 → (𝜃 → 𝜏)) |
ee112.4 | ⊢ (𝜓 → (𝜒 → (𝜏 → 𝜂))) |
Ref | Expression |
---|---|
ee112 | ⊢ (𝜑 → (𝜃 → 𝜂)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee112.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | a1d 25 | . 2 ⊢ (𝜑 → (𝜃 → 𝜓)) |
3 | ee112.2 | . . 3 ⊢ (𝜑 → 𝜒) | |
4 | 3 | a1d 25 | . 2 ⊢ (𝜑 → (𝜃 → 𝜒)) |
5 | ee112.3 | . 2 ⊢ (𝜑 → (𝜃 → 𝜏)) | |
6 | ee112.4 | . 2 ⊢ (𝜓 → (𝜒 → (𝜏 → 𝜂))) | |
7 | 2, 4, 5, 6 | ee222 37729 | 1 ⊢ (𝜑 → (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 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |