Theorem simp-4l 543

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 535	. 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  545  disjiun  4083  fnfi  7135  nninfisol  7332  swrdccatin1  11307  sumeq2  11921  zsumdc  11947  modfsummod  12021  prodeq2  12120  zproddc  12142  mulgval  13711  mplsubgfilemcl  14716  cncnp  14957  fsumcncntop  15294  dvmptfsum  15452  dvply2g  15493  logbgcd1irrap  15697  upgriswlkdc  16214  clwwlkccatlem  16254