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Mirrors > Home > MPE Home > Th. List > Mathboxes > e233 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 29-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e233.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
e233.2 | ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜏 ) |
e233.3 | ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜂 ) |
e233.4 | ⊢ (𝜒 → (𝜏 → (𝜂 → 𝜁))) |
Ref | Expression |
---|---|
e233 | ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜁 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e233.1 | . . . 4 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | 1 | dfvd2i 37822 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) |
3 | e233.2 | . . . 4 ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜏 ) | |
4 | 3 | dfvd3i 37829 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏))) |
5 | e233.3 | . . . 4 ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜂 ) | |
6 | 5 | dfvd3i 37829 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜂))) |
7 | e233.4 | . . 3 ⊢ (𝜒 → (𝜏 → (𝜂 → 𝜁))) | |
8 | 2, 4, 6, 7 | ee233 37746 | . 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜁))) |
9 | 8 | dfvd3ir 37830 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜃 ▶ 𝜁 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 37814 ( wvd3 37824 |
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 df-3an 1033 df-vd2 37815 df-vd3 37827 |
This theorem is referenced by: truniALTVD 38136 onfrALTlem2VD 38147 |
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