Theorem simp111 1321

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 1222	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant1 1151	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  tsmsxp  24479  ps-2b  40632  llncvrlpln2  40707  4atlem11b  40758  4atlem12b  40761  lplncvrlvol2  40765  lneq2at  40928  2lnat  40934  cdlemblem  40943  4atexlemex6  41224  cdleme24  41502  cdleme26ee  41510  cdlemg2idN  41746  cdlemg31c  41849  cdlemk26-3  42056  0ellimcdiv  46752