Theorem simp1ll 1243

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 772	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜑)
2	1	3ad2ant1 1139	1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  lspsolvlem  21142  1marepvsma1  22573  mdetunilem8  22609  madutpos  22632  bdayfinbndlem1  28484  ax5seg  29032  rabfodom  32600  measinblem  34411  btwnconn1lem2  36323  btwnconn1lem13  36334  athgt  39955  llnle  40017  lplnle  40039  lhpexle1  40507  lhpj1  40521  lhpat3  40545  ltrncnv  40645  cdleme16aN  40758  tendoicl  41295  cdlemk55b  41459  dihatexv  41837  dihglblem6  41839  limccog  46072  icccncfext  46337  stoweidlem31  46481  stoweidlem34  46484  stoweidlem49  46499  stoweidlem57  46507