Theorem simp2l2 1292

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

Assertion

Ref	Expression
simp2l2	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)

Proof of Theorem simp2l2

Step	Hyp	Ref	Expression
1		simpl2 1211	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	3ad2ant2 1152	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  poxp3  8160  btwnconn1lem9  36840  btwnconn1lem10  36841  btwnconn1lem11  36842  btwnconn1lem12  36843  2lplnja  40656  cdlemk21-2N  41928  cdlemk31  41933  cdlemk19xlem  41979  jm2.27  43994