Theorem simp131 1308

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp131	⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Proof of Theorem simp131

Step	Hyp	Ref	Expression
1		simp31 1209	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 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:  ax5seglem3  28964  exatleN  39361  3atlem1  39440  3atlem2  39441  3atlem5  39444  2llnjaN  39523  4atlem11b  39565  4atlem12b  39568  lplncvrlvol2  39572  dalemsea  39586  dath2  39694  cdlemblem  39750  dalawlem1  39828  lhpexle3lem  39968  4atexlemex6  40031  cdleme22f2  40304  cdleme22g  40305  cdlemg7aN  40582  cdlemg34  40669  cdlemj1  40778  cdlemk23-3  40859  cdlemk25-3  40861  cdlemk26b-3  40862  cdleml3N  40935