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Mirrors > Home > MPE Home > Th. List > simp3ll | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3ll | ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 767 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜑) | |
2 | 1 | 3ad2ant3 1134 | 1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 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: f1oiso2 7372 omeu 8622 ntrivcvgmul 15935 tsmsxp 24179 tgqioo 24836 ovolunlem2 25547 plyadd 26271 plymul 26272 coeeu 26279 nosupbnd1lem2 27769 noinfbnd1lem2 27784 tghilberti2 28661 btwnconn1lem2 36070 btwnconn1lem3 36071 btwnconn1lem12 36080 athgt 39439 2llnjN 39550 4atlem12b 39594 lncmp 39766 cdlema2N 39775 cdlemc2 40175 cdleme5 40223 cdleme11a 40243 cdleme21ct 40312 cdleme21 40320 cdleme22eALTN 40328 cdleme24 40335 cdleme27cl 40349 cdleme27a 40350 cdleme28 40356 cdleme36a 40443 cdleme42b 40461 cdleme48fvg 40483 cdlemf 40546 cdlemk39 40899 cdlemkid1 40905 dihlsscpre 41217 dihord4 41241 dihord5apre 41245 dihmeetlem20N 41309 mapdh9a 41772 pellex 42823 jm2.27 42997 |
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