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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 43354 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜒 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ( wvd3 43348 |
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 398 df-3an 1090 df-vd3 43351 |
This theorem is referenced by: suctrALT2VD 43597 en3lplem2VD 43605 exbirVD 43614 exbiriVD 43615 rspsbc2VD 43616 tratrbVD 43622 ssralv2VD 43627 imbi12VD 43634 imbi13VD 43635 truniALTVD 43639 trintALTVD 43641 onfrALTlem2VD 43650 |
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