Theorem simp1rl 1245

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 776	. 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2ant1 1139	1 ⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  f1imass  7215  smo11  8301  zsupss  12885  lsmcv  21141  lspsolvlem  21142  mat2pmatghm  22720  mat2pmatmul  22721  plyadd  26207  plymul  26208  coeeu  26215  aannenlem1  26319  logexprlim  27213  ax5seglem6  29028  ax5seg  29032  mdetpmtr1  34014  mdetpmtr2  34015  wsuclem  36058  btwnconn1lem2  36323  btwnconn1lem3  36324  btwnconn1lem4  36325  btwnconn1lem12  36333  lshpsmreu  39608  2llnmat  40023  lvolex3N  40037  lnjatN  40279  pclfinclN  40449  lhpat3  40545  cdlemd6  40702  cdlemfnid  41063  cdlemk19ylem  41429  dihlsscpre  41733  dih1dimb2  41740  dihglblem6  41839  pellex  43287  tfsconcatrn  43794  mullimc  46068  mullimcf  46075  limcperiod  46080  cncfshift  46324  cncfperiod  46329  nprmmul2  48010