Theorem simp112 1322

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 1223	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant1 1151	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜓)

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:  axcontlem4  29545  ps-2b  40539  llncvrlpln2  40614  4atlem11b  40665  4atlem12b  40668  2lnat  40841  cdlemblem  40850  4atexlemex6  41131  cdleme24  41409  cdleme26ee  41417  cdlemg2idN  41653  cdlemg31c  41756  cdlemk26-3  41963  dihglblem2N  42351  0ellimcdiv  46658