Theorem simp1lr 1238

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 768	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant1 1133	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

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:  lspsolvlem  21072  dmatcrng  22410  scmatcrng  22429  1marepvsma1  22491  mdetunilem7  22526  mat2pmatghm  22638  pmatcollpwscmatlem2  22698  mp2pm2mplem4  22717  ax5seg  28909  measinblem  34223  btwnconn1lem13  36112  athgt  39474  llnle  39536  lplnle  39558  lhpexle1  40026  lhpat3  40064  tendoicl  40814  cdlemk55b  40978  pellex  42847  ssfiunibd  45329  mullimc  45635  mullimcf  45642  icccncfext  45904  etransclem32  46283  uhgrimisgrgriclem  47940