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Mirrors > Home > MPE Home > Th. List > Mathboxes > e000 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. The non-virtual deduction form of e000 38015 is the virtual deduction form. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e000.1 | ⊢ 𝜑 |
e000.2 | ⊢ 𝜓 |
e000.3 | ⊢ 𝜒 |
e000.4 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
e000 | ⊢ 𝜃 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e000.3 | . 2 ⊢ 𝜒 | |
2 | e000.1 | . . 3 ⊢ 𝜑 | |
3 | e000.2 | . . 3 ⊢ 𝜓 | |
4 | e000.4 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
5 | 2, 3, 4 | mp2 9 | . 2 ⊢ (𝜒 → 𝜃) |
6 | 1, 5 | ax-mp 5 | 1 ⊢ 𝜃 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 |
This theorem is referenced by: ax6e2ndeqVD 38167 |
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