Theorem simp2l3 1293

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

Assertion

Ref	Expression
simp2l3	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)

Proof of Theorem simp2l3

Step	Hyp	Ref	Expression
1		simpl3 1212	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒)
2	1	3ad2ant2 1152	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)

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  8152  btwnconn1lem8  36625  btwnconn1lem12  36629  2lplnja  40453  cdlemk21-2N  41725  cdlemk19xlem  41776  jm2.27  43795