Theorem simp132 1310

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

Assertion

Ref	Expression
simp132	⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜓)

Proof of Theorem simp132

Step	Hyp	Ref	Expression
1		simp32 1211	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜓)

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  28858  3atlem1  39477  3atlem2  39478  3atlem5  39481  2llnjaN  39560  4atlem11b  39602  4atlem12b  39605  lplncvrlvol2  39609  dalemtea  39624  dath2  39731  cdlemblem  39787  dalawlem1  39865  lhpexle3lem  40005  4atexlemex6  40068  cdleme22f2  40341  cdleme22g  40342  cdlemg7aN  40619  cdlemg34  40706  cdlemj1  40815  cdlemk23-3  40896  cdlemk25-3  40898  cdlemk26b-3  40899