Theorem simp131 1309

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 1210	. 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 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 207  df-an 396  df-3an 1088

This theorem is referenced by:  ax5seglem3  28915  exatleN  39428  3atlem1  39507  3atlem2  39508  3atlem5  39511  2llnjaN  39590  4atlem11b  39632  4atlem12b  39635  lplncvrlvol2  39639  dalemsea  39653  dath2  39761  cdlemblem  39817  dalawlem1  39895  lhpexle3lem  40035  4atexlemex6  40098  cdleme22f2  40371  cdleme22g  40372  cdlemg7aN  40649  cdlemg34  40736  cdlemj1  40845  cdlemk23-3  40926  cdlemk25-3  40928  cdlemk26b-3  40929  cdleml3N  41002