Theorem simp1ll 1233

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp1ll	⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Proof of Theorem simp1ll

Step	Hyp	Ref	Expression
1		simpll 765	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜑)
2	1	3ad2ant1 1130	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

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  21037  1marepvsma1  22505  mdetunilem8  22541  madutpos  22564  ax5seg  28769  rabfodom  32322  measinblem  33872  btwnconn1lem2  35717  btwnconn1lem13  35728  athgt  38961  llnle  39023  lplnle  39045  lhpexle1  39513  lhpj1  39527  lhpat3  39551  ltrncnv  39651  cdleme16aN  39764  tendoicl  40301  cdlemk55b  40465  dihatexv  40843  dihglblem6  40845  limccog  45037  icccncfext  45304  stoweidlem31  45448  stoweidlem34  45451  stoweidlem49  45466  stoweidlem57  45474