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  28834  exatleN  39371  3atlem1  39450  3atlem2  39451  3atlem5  39454  2llnjaN  39533  4atlem11b  39575  4atlem12b  39578  lplncvrlvol2  39582  dalemsea  39596  dath2  39704  cdlemblem  39760  dalawlem1  39838  lhpexle3lem  39978  4atexlemex6  40041  cdleme22f2  40314  cdleme22g  40315  cdlemg7aN  40592  cdlemg34  40679  cdlemj1  40788  cdlemk23-3  40869  cdlemk25-3  40871  cdlemk26b-3  40872  cdleml3N  40945