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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 771 | . 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜑) | |
2 | 1 | 3ad2ant3 1134 | 1 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1086 |
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 207 df-an 396 df-3an 1088 |
This theorem is referenced by: omeu 8621 hashbclem 14487 ntrivcvgmul 15934 tsmsxp 24178 tgqioo 24835 ovolunlem2 25546 plyadd 26270 plymul 26271 coeeu 26278 nosupbnd1lem2 27768 noinfbnd1lem2 27783 tghilberti2 28660 cvmlift2lem10 35296 btwnconn1lem1 36068 btwnconn1lem2 36069 btwnconn1lem12 36079 lplnexllnN 39546 2llnjN 39549 4atlem12b 39593 lplncvrlvol2 39597 lncmp 39765 cdlema2N 39774 cdlemc2 40174 cdleme11a 40242 cdleme22eALTN 40327 cdleme24 40334 cdleme27a 40349 cdleme27N 40351 cdleme28 40355 cdlemefs29bpre0N 40398 cdlemefs29bpre1N 40399 cdlemefs29cpre1N 40400 cdlemefs29clN 40401 cdlemefs32fvaN 40404 cdlemefs32fva1 40405 cdleme36m 40443 cdleme39a 40447 cdleme17d3 40478 cdleme50trn2 40533 cdlemg36 40696 cdlemj3 40805 cdlemkfid1N 40903 cdlemkid1 40904 cdlemk19ylem 40912 cdlemk19xlem 40924 dihlsscpre 41216 dihord4 41240 dihatlat 41316 mapdh9a 41771 jm2.27 42996 |
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