Theorem simp132 1311

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 1212	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant1 1134	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜓)

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  29014  3atlem1  39943  3atlem2  39944  3atlem5  39947  2llnjaN  40026  4atlem11b  40068  4atlem12b  40071  lplncvrlvol2  40075  dalemtea  40090  dath2  40197  cdlemblem  40253  dalawlem1  40331  lhpexle3lem  40471  4atexlemex6  40534  cdleme22f2  40807  cdleme22g  40808  cdlemg7aN  41085  cdlemg34  41172  cdlemj1  41281  cdlemk23-3  41362  cdlemk25-3  41364  cdlemk26b-3  41365