Theorem simp3r3 1283

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

Assertion

Ref	Expression
simp3r3	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simp3r3

Step	Hyp	Ref	Expression
1		simpr3 1196	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1087

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 206  df-an 397  df-3an 1089

This theorem is referenced by:  nllyrest  22989  cdlemblem  38659  cdleme21  39203  cdleme22b  39207  cdleme40m  39333  cdlemg34  39578  cdlemk5u  39727  cdlemk6u  39728  cdlemk21N  39739  cdlemk20  39740  cdlemk26b-3  39771  cdlemk26-3  39772  cdlemk28-3  39774  cdlemky  39792  cdlemk11t  39812  cdlemkyyN  39828  dihmeetlem20N  40192  stoweidlem56  44762