Theorem simp1lr 1244

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

Assertion

Ref	Expression
simp1lr	⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Proof of Theorem simp1lr

Step	Hyp	Ref	Expression
1		simplr 774	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant1 1139	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

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:  lspsolvlem  21142  dmatcrng  22492  scmatcrng  22511  1marepvsma1  22573  mdetunilem7  22608  mat2pmatghm  22720  pmatcollpwscmatlem2  22780  mp2pm2mplem4  22799  ax5seg  29032  measinblem  34411  btwnconn1lem13  36334  athgt  39955  llnle  40017  lplnle  40039  lhpexle1  40507  lhpat3  40545  tendoicl  41295  cdlemk55b  41459  pellex  43287  ssfiunibd  45764  mullimc  46068  mullimcf  46075  icccncfext  46337  etransclem32  46716  uhgrimisgrgriclem  48428