Theorem simp111 1304

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 1205	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant1 1134	1 ⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

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:  tsmsxp  24098  ps-2b  39919  llncvrlpln2  39994  4atlem11b  40045  4atlem12b  40048  lplncvrlvol2  40052  lneq2at  40215  2lnat  40221  cdlemblem  40230  4atexlemex6  40511  cdleme24  40789  cdleme26ee  40797  cdlemg2idN  41033  cdlemg31c  41136  cdlemk26-3  41343  0ellimcdiv  46081