Theorem simp1ll 1236

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 766	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

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  21112  1marepvsma1  22537  mdetunilem8  22573  madutpos  22596  ax5seg  28883  rabfodom  32452  measinblem  34180  btwnconn1lem2  36048  btwnconn1lem13  36059  athgt  39417  llnle  39479  lplnle  39501  lhpexle1  39969  lhpj1  39983  lhpat3  40007  ltrncnv  40107  cdleme16aN  40220  tendoicl  40757  cdlemk55b  40921  dihatexv  41299  dihglblem6  41301  limccog  45592  icccncfext  45859  stoweidlem31  46003  stoweidlem34  46006  stoweidlem49  46021  stoweidlem57  46029