| Mathbox for Alan Sare |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > in3 | Structured version Visualization version GIF version | ||
| Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| in3.1 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
| Ref | Expression |
|---|---|
| in3 | ⊢ ( 𝜑 , 𝜓 ▶ (𝜒 → 𝜃) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | in3.1 | . . 3 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) | |
| 2 | 1 | dfvd3i 44612 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| 3 | 2 | dfvd2ir 44606 | 1 ⊢ ( 𝜑 , 𝜓 ▶ (𝜒 → 𝜃) ) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ( wvd2 44597 ( wvd3 44607 |
| 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 207 df-an 396 df-3an 1089 df-vd2 44598 df-vd3 44610 |
| This theorem is referenced by: e223 44655 suctrALT2VD 44856 en3lplem2VD 44864 exbirVD 44873 exbiriVD 44874 rspsbc2VD 44875 tratrbVD 44881 ssralv2VD 44886 imbi12VD 44893 imbi13VD 44894 truniALTVD 44898 trintALTVD 44900 onfrALTlem2VD 44909 |
| Copyright terms: Public domain | W3C validator |