Theorem simp221 1332

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

Assertion

Ref	Expression
simp221	⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜑)

Proof of Theorem simp221

Step	Hyp	Ref	Expression
1		simp21 1224	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant2 1151	1 ⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1102

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 401  df-3an 1104

This theorem is used by:  4atexlemcnd  40874  cdleme26eALTN  41163  cdleme27a  41169  cdlemk23-3  41704  cdlemk25-3  41706  cdlemk27-3  41709