Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 790 | . 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜑) | |
2 | 1 | 3ad2ant3 1077 | 1 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
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 196 df-an 385 df-3an 1033 |
This theorem is referenced by: omeu 7552 hashbclem 13093 ntrivcvgmul 14473 tsmsxp 21768 tgqioo 22411 ovolunlem2 23073 plyadd 23777 plymul 23778 coeeu 23785 tghilberti2 25333 cvmlift2lem10 30548 btwnconn1lem1 31364 btwnconn1lem2 31365 btwnconn1lem12 31375 lplnexllnN 33868 2llnjN 33871 4atlem12b 33915 lplncvrlvol2 33919 lncmp 34087 cdlema2N 34096 cdlemc2 34497 cdleme11a 34565 cdleme22eALTN 34651 cdleme24 34658 cdleme27a 34673 cdleme27N 34675 cdleme28 34679 cdlemefs29bpre0N 34722 cdlemefs29bpre1N 34723 cdlemefs29cpre1N 34724 cdlemefs29clN 34725 cdlemefs32fvaN 34728 cdlemefs32fva1 34729 cdleme36m 34767 cdleme39a 34771 cdleme17d3 34802 cdleme50trn2 34857 cdlemg36 35020 cdlemj3 35129 cdlemkfid1N 35227 cdlemkid1 35228 cdlemk19ylem 35236 cdlemk19xlem 35248 dihlsscpre 35541 dihord4 35565 dihatlat 35641 mapdh9a 36097 jm2.27 36593 |
Copyright terms: Public domain | W3C validator |