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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > idn3 | Structured version Visualization version GIF version |
Description: Virtual deduction identity rule for three virtual hypotheses. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
idn3 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜒 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd 24 | . . 3 ⊢ (𝜓 → (𝜒 → 𝜒)) | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜒))) |
3 | 2 | dfvd3ir 43339 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜒 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd3 43333 |
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 206 df-an 397 df-3an 1089 df-vd3 43336 |
This theorem is referenced by: suctrALT2VD 43582 en3lplem2VD 43590 exbirVD 43599 exbiriVD 43600 rspsbc2VD 43601 tratrbVD 43607 ssralv2VD 43612 imbi12VD 43619 imbi13VD 43620 truniALTVD 43624 trintALTVD 43626 onfrALTlem2VD 43635 |
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