Theorem simp1lr 1239

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 769	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant1 1134	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  lspsolvlem  21130  dmatcrng  22476  scmatcrng  22495  1marepvsma1  22557  mdetunilem7  22592  mat2pmatghm  22704  pmatcollpwscmatlem2  22764  mp2pm2mplem4  22783  ax5seg  29026  measinblem  34385  btwnconn1lem13  36302  athgt  39913  llnle  39975  lplnle  39997  lhpexle1  40465  lhpat3  40503  tendoicl  41253  cdlemk55b  41417  pellex  43278  ssfiunibd  45757  mullimc  46061  mullimcf  46068  icccncfext  46330  etransclem32  46709  uhgrimisgrgriclem  48403