Theorem simp311 1321

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

Assertion

Ref	Expression
simp311	⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑)

Proof of Theorem simp311

Step	Hyp	Ref	Expression
1		simp11 1204	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1086

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 1088

This theorem is referenced by:  dalem-clpjq  39656  dath2  39756  cdleme26e  40378  cdleme38m  40482  cdleme38n  40483  cdleme39n  40485  cdlemg28b  40722  cdlemk7  40867  cdlemk11  40868  cdlemk12  40869  cdlemk7u  40889  cdlemk11u  40890  cdlemk12u  40891  cdlemk22  40912  cdlemk23-3  40921  cdlemk25-3  40923