Theorem simp111 1315

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

Assertion

Ref	Expression
simp111	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Proof of Theorem simp111

Step	Hyp	Ref	Expression
1		simp11 1216	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant1 1145	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  tsmsxp  24202  ps-2b  40066  llncvrlpln2  40141  4atlem11b  40192  4atlem12b  40195  lplncvrlvol2  40199  lneq2at  40362  2lnat  40368  cdlemblem  40377  4atexlemex6  40658  cdleme24  40936  cdleme26ee  40944  cdlemg2idN  41180  cdlemg31c  41283  cdlemk26-3  41490  0ellimcdiv  46183