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Mirrors > Home > MPE Home > Th. List > Mathboxes > e13 | Structured version Visualization version GIF version |
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e13.1 | ⊢ ( 𝜑 ▶ 𝜓 ) |
e13.2 | ⊢ ( 𝜑 , 𝜒 , 𝜃 ▶ 𝜏 ) |
e13.3 | ⊢ (𝜓 → (𝜏 → 𝜂)) |
Ref | Expression |
---|---|
e13 | ⊢ ( 𝜑 , 𝜒 , 𝜃 ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e13.1 | . . 3 ⊢ ( 𝜑 ▶ 𝜓 ) | |
2 | 1 | vd13 40812 | . 2 ⊢ ( 𝜑 , 𝜒 , 𝜃 ▶ 𝜓 ) |
3 | e13.2 | . 2 ⊢ ( 𝜑 , 𝜒 , 𝜃 ▶ 𝜏 ) | |
4 | e13.3 | . 2 ⊢ (𝜓 → (𝜏 → 𝜂)) | |
5 | 2, 3, 4 | e33 40945 | 1 ⊢ ( 𝜑 , 𝜒 , 𝜃 ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd1 40780 ( wvd3 40798 |
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 208 df-an 397 df-3an 1081 df-vd1 40781 df-vd3 40801 |
This theorem is referenced by: e13an 40960 en3lplem2VD 41055 rspsbc2VD 41066 ssralv2VD 41077 imbi12VD 41084 imbi13VD 41085 truniALTVD 41089 |
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