Theorem simp112 1299

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 1200	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant1 1129	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1083

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 399  df-3an 1085

This theorem is referenced by:  axcontlem4  26752  ps-2b  36617  llncvrlpln2  36692  4atlem11b  36743  4atlem12b  36746  2lnat  36919  cdlemblem  36928  4atexlemex6  37209  cdleme24  37487  cdleme26ee  37495  cdlemg2idN  37731  cdlemg31c  37834  cdlemk26-3  38041  dihglblem2N  38429  0ellimcdiv  41928