Theorem simp1rl 1239

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 770	. 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜑)

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:  f1imass  7210  smo11  8296  zsupss  12850  lsmcv  21096  lspsolvlem  21097  mat2pmatghm  22674  mat2pmatmul  22675  plyadd  26178  plymul  26179  coeeu  26186  aannenlem1  26292  logexprlim  27192  ax5seglem6  29007  ax5seg  29011  mdetpmtr1  33980  mdetpmtr2  33981  wsuclem  36017  btwnconn1lem2  36282  btwnconn1lem3  36283  btwnconn1lem4  36284  btwnconn1lem12  36292  lshpsmreu  39369  2llnmat  39784  lvolex3N  39798  lnjatN  40040  pclfinclN  40210  lhpat3  40306  cdlemd6  40463  cdlemfnid  40824  cdlemk19ylem  41190  dihlsscpre  41494  dih1dimb2  41501  dihglblem6  41600  pellex  43077  tfsconcatrn  43584  mullimc  45862  mullimcf  45869  limcperiod  45874  cncfshift  46118  cncfperiod  46123