Theorem simp311 1316

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 1199	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1131	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 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:  dalem-clpjq  36772  dath2  36872  cdleme26e  37494  cdleme38m  37598  cdleme38n  37599  cdleme39n  37601  cdlemg28b  37838  cdlemk7  37983  cdlemk11  37984  cdlemk12  37985  cdlemk7u  38005  cdlemk11u  38006  cdlemk12u  38007  cdlemk22  38028  cdlemk23-3  38037  cdlemk25-3  38039