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 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  28947  exatleN  39407  3atlem1  39486  3atlem2  39487  3atlem5  39490  2llnjaN  39569  4atlem11b  39611  4atlem12b  39614  lplncvrlvol2  39618  dalemsea  39632  dath2  39740  cdlemblem  39796  dalawlem1  39874  lhpexle3lem  40014  4atexlemex6  40077  cdleme22f2  40350  cdleme22g  40351  cdlemg7aN  40628  cdlemg34  40715  cdlemj1  40824  cdlemk23-3  40905  cdlemk25-3  40907  cdlemk26b-3  40908  cdleml3N  40981