Theorem simp112 1302

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 1203	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant1 1132	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1086

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 396  df-3an 1088

This theorem is referenced by:  axcontlem4  28659  ps-2b  38819  llncvrlpln2  38894  4atlem11b  38945  4atlem12b  38948  2lnat  39121  cdlemblem  39130  4atexlemex6  39411  cdleme24  39689  cdleme26ee  39697  cdlemg2idN  39933  cdlemg31c  40036  cdlemk26-3  40243  dihglblem2N  40631  0ellimcdiv  44826