Theorem simp1lr 1234

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 767	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant1 1130	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1084

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 395  df-3an 1086

This theorem is referenced by:  lspsolvlem  21125  dmatcrng  22498  scmatcrng  22517  1marepvsma1  22579  mdetunilem7  22614  mat2pmatghm  22726  pmatcollpwscmatlem2  22786  mp2pm2mplem4  22805  ax5seg  28875  measinblem  34055  btwnconn1lem13  35925  athgt  39157  llnle  39219  lplnle  39241  lhpexle1  39709  lhpat3  39747  tendoicl  40497  cdlemk55b  40661  pellex  42510  ssfiunibd  44942  mullimc  45255  mullimcf  45262  icccncfext  45526  etransclem32  45905  uhgrimisgrgriclem  47495