Theorem simp1l1 1266

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

Assertion

Ref	Expression
simp1l1	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Proof of Theorem simp1l1

Step	Hyp	Ref	Expression
1		simpl1 1191	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  poxp3  8191  mapxpen  9209  hash7g  14535  lsmcv  21166  sltlpss  27963  archiabl  33178  trisegint  35992  linethru  36117  hlrelat3  39369  cvrval3  39370  cvrval4N  39371  2atlt  39396  atbtwnex  39405  1cvratlt  39431  atcvrlln2  39476  atcvrlln  39477  2llnmat  39481  lplnexllnN  39521  lvolnlelpln  39542  lnjatN  39737  lncvrat  39739  lncmp  39740  cdlemd9  40163  dihord5b  41216  dihmeetALTN  41284  dih1dimatlem0  41285  mapdrvallem2  41602  grumnudlem  44254