Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > ee31an | Structured version Visualization version GIF version |
Description: e31an 42046 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee31an.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
ee31an.2 | ⊢ (𝜑 → 𝜏) |
ee31an.3 | ⊢ ((𝜃 ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
ee31an | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee31an.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | ee31an.2 | . . . 4 ⊢ (𝜑 → 𝜏) | |
3 | 2 | a1d 25 | . . 3 ⊢ (𝜑 → (𝜒 → 𝜏)) |
4 | 3 | a1d 25 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏))) |
5 | ee31an.3 | . 2 ⊢ ((𝜃 ∧ 𝜏) → 𝜂) | |
6 | 1, 4, 5 | ee33an 42029 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |