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Mirrors > Home > MPE Home > Th. List > simp3rr | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3rr | ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simprr 771 | . 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜓) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 ∧ w3a 1083 |
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 209 df-an 399 df-3an 1085 |
This theorem is referenced by: omeu 8211 ntrivcvgmul 15258 tsmsxp 22763 tgqioo 23408 ovolunlem2 24099 plyadd 24807 plymul 24808 coeeu 24815 tghilberti2 26424 cvmlift2lem10 32559 nosupbnd1lem2 33209 btwnconn1lem1 33548 lplnexllnN 36715 2llnjN 36718 4atlem12b 36762 lplncvrlvol2 36766 lncmp 36934 cdlema2N 36943 cdleme11a 37411 cdleme24 37503 cdleme28 37524 cdlemefr29bpre0N 37557 cdlemefr29clN 37558 cdlemefr32fvaN 37560 cdlemefr32fva1 37561 cdlemefs29bpre0N 37567 cdlemefs29bpre1N 37568 cdlemefs29cpre1N 37569 cdlemefs29clN 37570 cdlemefs32fvaN 37573 cdlemefs32fva1 37574 cdleme36m 37612 cdleme17d3 37647 cdlemg36 37865 cdlemj3 37974 cdlemkid1 38073 cdlemk19ylem 38081 cdlemk19xlem 38093 dihlsscpre 38385 dihord4 38409 dihmeetlem1N 38441 dihatlat 38485 jm2.27 39625 |
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