Theorem simp111 1190

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 1091	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant1 1082	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  tsmsxp  21958  ps-2b  34768  llncvrlpln2  34843  4atlem11b  34894  4atlem12b  34897  lplncvrlvol2  34901  lneq2at  35064  2lnat  35070  cdlemblem  35079  4atexlemex6  35360  cdleme24  35640  cdleme26ee  35648  cdlemg2idN  35884  cdlemg31c  35987  cdlemk26-3  36194  0ellimcdiv  39881