Theorem simp231 1313

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

Assertion

Ref	Expression
simp231	⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜁) → 𝜑)

Proof of Theorem simp231

Step	Hyp	Ref	Expression
1		simp31 1205	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant2 1130	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  cdlemd4  37331  cdleme21ct  37459  cdleme21e  37461  cdleme21f  37462  cdleme21i  37465  cdleme26eALTN  37491  cdlemk23-3  38032  cdlemk25-3  38034