Theorem simp113 1304

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 1205	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant1 1133	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  axcontlem4  29000  llncvrlpln2  39514  4atlem12b  39568  2lnat  39741  cdlemblem  39750  4atexlemex6  40031  cdleme24  40309  cdleme26ee  40317  cdlemg2idN  40553  dihglblem2N  41251  0ellimcdiv  45570  limclner  45572