Theorem simp1lr 1236

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 1132	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  21161  dmatcrng  22523  scmatcrng  22542  1marepvsma1  22604  mdetunilem7  22639  mat2pmatghm  22751  pmatcollpwscmatlem2  22811  mp2pm2mplem4  22830  ax5seg  28967  measinblem  34200  btwnconn1lem13  36080  athgt  39438  llnle  39500  lplnle  39522  lhpexle1  39990  lhpat3  40028  tendoicl  40778  cdlemk55b  40942  pellex  42822  ssfiunibd  45259  mullimc  45571  mullimcf  45578  icccncfext  45842  etransclem32  46221  uhgrimisgrgriclem  47835