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Mirrors > Home > MPE Home > Th. List > simp3rl | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3rl | ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simprl 794 | . 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜑) | |
2 | 1 | 3ad2ant3 1084 | 1 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 ∧ w3a 1037 |
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 197 df-an 386 df-3an 1039 |
This theorem is referenced by: omeu 7665 hashbclem 13236 ntrivcvgmul 14634 tsmsxp 21958 tgqioo 22603 ovolunlem2 23266 plyadd 23973 plymul 23974 coeeu 23981 tghilberti2 25533 cvmlift2lem10 31294 nosupbnd1lem2 31855 btwnconn1lem1 32194 btwnconn1lem2 32195 btwnconn1lem12 32205 lplnexllnN 34850 2llnjN 34853 4atlem12b 34897 lplncvrlvol2 34901 lncmp 35069 cdlema2N 35078 cdlemc2 35479 cdleme11a 35547 cdleme22eALTN 35633 cdleme24 35640 cdleme27a 35655 cdleme27N 35657 cdleme28 35661 cdlemefs29bpre0N 35704 cdlemefs29bpre1N 35705 cdlemefs29cpre1N 35706 cdlemefs29clN 35707 cdlemefs32fvaN 35710 cdlemefs32fva1 35711 cdleme36m 35749 cdleme39a 35753 cdleme17d3 35784 cdleme50trn2 35839 cdlemg36 36002 cdlemj3 36111 cdlemkfid1N 36209 cdlemkid1 36210 cdlemk19ylem 36218 cdlemk19xlem 36230 dihlsscpre 36523 dihord4 36547 dihatlat 36623 mapdh9a 37079 jm2.27 37575 |
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