Theorem simp112 1301

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

Assertion

Ref	Expression
simp112	⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Proof of Theorem simp112

Step	Hyp	Ref	Expression
1		simp12 1202	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant1 1131	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1085

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 1087

This theorem is referenced by:  axcontlem4  28492  ps-2b  38656  llncvrlpln2  38731  4atlem11b  38782  4atlem12b  38785  2lnat  38958  cdlemblem  38967  4atexlemex6  39248  cdleme24  39526  cdleme26ee  39534  cdlemg2idN  39770  cdlemg31c  39873  cdlemk26-3  40080  dihglblem2N  40468  0ellimcdiv  44663