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Mirrors > Home > MPE Home > Th. List > imp4b | Structured version Visualization version GIF version |
Description: An importation inference. (Contributed by NM, 26-Apr-1994.) Shorten imp4a 424. (Revised by Wolf Lammen, 19-Jul-2021.) |
Ref | Expression |
---|---|
imp4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Ref | Expression |
---|---|
imp4b | ⊢ ((𝜑 ∧ 𝜓) → ((𝜒 ∧ 𝜃) → 𝜏)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp4.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | 1 | imp 408 | . 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → (𝜃 → 𝜏))) |
3 | 2 | impd 412 | 1 ⊢ ((𝜑 ∧ 𝜓) → ((𝜒 ∧ 𝜃) → 𝜏)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 |
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 |
This theorem is referenced by: imp4a 424 imp43 429 imp5g 443 pm2.61da3ne 3032 onmindif 6457 oaordex 8558 pssnn 9168 pssnnOLD 9265 alephval3 10105 dfac5 10123 dfac2b 10125 coftr 10268 zorn2lem6 10496 addcanpi 10894 mulcanpi 10895 ltmpi 10899 ltexprlem6 11036 axpre-sup 11164 bndndx 12471 dmdprdd 19869 lssssr 20564 coe1fzgsumdlem 21825 evl1gsumdlem 21875 1stcrest 22957 upgrreslem 28592 umgrreslem 28593 mdsymlem3 31689 mdsymlem6 31692 sumdmdlem 31702 mclsax 34591 mclsppslem 34605 disjlem17 37717 prtlem17 37794 cvratlem 38340 paddidm 38760 pmodlem2 38766 pclfinclN 38869 onexoegt 42041 icceuelpart 46152 |
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