Theorem simp1rl 1240

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp1rl	⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Proof of Theorem simp1rl

Step	Hyp	Ref	Expression
1		simprl 771	. 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2ant1 1134	1 ⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  f1imass  7212  smo11  8298  zsupss  12854  lsmcv  21100  lspsolvlem  21101  mat2pmatghm  22678  mat2pmatmul  22679  plyadd  26182  plymul  26183  coeeu  26190  aannenlem1  26296  logexprlim  27196  ax5seglem6  28990  ax5seg  28994  mdetpmtr1  33961  mdetpmtr2  33962  wsuclem  35998  btwnconn1lem2  36263  btwnconn1lem3  36264  btwnconn1lem4  36265  btwnconn1lem12  36273  lshpsmreu  39406  2llnmat  39821  lvolex3N  39835  lnjatN  40077  pclfinclN  40247  lhpat3  40343  cdlemd6  40500  cdlemfnid  40861  cdlemk19ylem  41227  dihlsscpre  41531  dih1dimb2  41538  dihglblem6  41637  pellex  43113  tfsconcatrn  43620  mullimc  45898  mullimcf  45905  limcperiod  45910  cncfshift  46154  cncfperiod  46159