Theorem simp3r1 1169

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

Assertion

Ref	Expression
simp3r1	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Proof of Theorem simp3r1

Step	Hyp	Ref	Expression
1		simpr1 1067	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1084	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 384   ∧ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  nllyrest  21289  segletr  32221  cdlemblem  35079  cdleme21  35625  cdleme22b  35629  cdleme40m  35755  cdlemg34  36000  cdlemk5u  36149  cdlemk6u  36150  cdlemk21N  36161  cdlemk20  36162  cdlemk26b-3  36193  cdlemk26-3  36194  cdlemk28-3  36196  cdlemk37  36202  cdlemky  36214  cdlemk11t  36234  cdlemkyyN  36250  dihmeetlem20N  36615  stoweidlem56  40273