Theorem simp113 1301

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

Assertion

Ref	Expression
simp113	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Proof of Theorem simp113

Step	Hyp	Ref	Expression
1		simp13 1202	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant1 1130	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1084

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 206  df-an 395  df-3an 1086

This theorem is referenced by:  axcontlem4  28901  llncvrlpln2  39256  4atlem12b  39310  2lnat  39483  cdlemblem  39492  4atexlemex6  39773  cdleme24  40051  cdleme26ee  40059  cdlemg2idN  40295  dihglblem2N  40993  0ellimcdiv  45270  limclner  45272