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 1134	1 ⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 397   ∧ w3a 1088

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 206  df-an 398  df-3an 1090

This theorem is referenced by:  f1imass  7263  smo11  8364  zsupss  12921  lsmcv  20754  lspsolvlem  20755  mat2pmatghm  22232  mat2pmatmul  22233  plyadd  25731  plymul  25732  coeeu  25739  aannenlem1  25841  logexprlim  26728  ax5seglem6  28192  ax5seg  28196  mdetpmtr1  32803  mdetpmtr2  32804  wsuclem  34797  btwnconn1lem2  35060  btwnconn1lem3  35061  btwnconn1lem4  35062  btwnconn1lem12  35070  lshpsmreu  37979  2llnmat  38395  lvolex3N  38409  lnjatN  38651  pclfinclN  38821  lhpat3  38917  cdlemd6  39074  cdlemfnid  39435  cdlemk19ylem  39801  dihlsscpre  40105  dih1dimb2  40112  dihglblem6  40211  pellex  41573  tfsconcatrn  42092  mullimc  44332  mullimcf  44339  limcperiod  44344  cncfshift  44590  cncfperiod  44595