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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 41918 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | dfvd2ir 41912 | 1 ⊢ ( 𝜑 , 𝜓 ▶ (𝜒 → 𝜃) ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd2 41903 ( wvd3 41913 |
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 df-3an 1091 df-vd2 41904 df-vd3 41916 |
This theorem is referenced by: e223 41961 suctrALT2VD 42162 en3lplem2VD 42170 exbirVD 42179 exbiriVD 42180 rspsbc2VD 42181 tratrbVD 42187 ssralv2VD 42192 imbi12VD 42199 imbi13VD 42200 truniALTVD 42204 trintALTVD 42206 onfrALTlem2VD 42215 |
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