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  39616  dath2  39716  cdleme26e  40338  cdleme38m  40442  cdleme38n  40443  cdleme39n  40445  cdlemg28b  40682  cdlemk7  40827  cdlemk11  40828  cdlemk12  40829  cdlemk7u  40849  cdlemk11u  40850  cdlemk12u  40851  cdlemk22  40872  cdlemk23-3  40881  cdlemk25-3  40883