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 1134	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 397   ∧ w3a 1088

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 398  df-3an 1090

This theorem is referenced by:  lspsolvlem  20755  dmatcrng  22004  scmatcrng  22023  1marepvsma1  22085  mdetunilem7  22120  mat2pmatghm  22232  pmatcollpwscmatlem2  22292  mp2pm2mplem4  22311  ax5seg  28196  measinblem  33218  btwnconn1lem13  35071  athgt  38327  llnle  38389  lplnle  38411  lhpexle1  38879  lhpat3  38917  tendoicl  39667  cdlemk55b  39831  pellex  41573  ssfiunibd  44019  mullimc  44332  mullimcf  44339  icccncfext  44603  etransclem32  44982