Theorem simp-4l 541

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
simp-4l	⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Proof of Theorem simp-4l

Step	Hyp	Ref	Expression
1		simplll 533	. 2 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	adantr 276	1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  simp-5l  543  disjiun  4081  fnfi  7129  nninfisol  7326  swrdccatin1  11299  sumeq2  11913  zsumdc  11938  modfsummod  12012  prodeq2  12111  zproddc  12133  mulgval  13702  mplsubgfilemcl  14706  cncnp  14947  fsumcncntop  15284  dvmptfsum  15442  dvply2g  15483  logbgcd1irrap  15687  upgriswlkdc  16171  clwwlkccatlem  16209