Theorem simp3r3 1280

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 1193	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1132	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1084

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 210  df-an 400  df-3an 1086

This theorem is referenced by:  nllyrest  22091  cdlemblem  37089  cdleme21  37633  cdleme22b  37637  cdleme40m  37763  cdlemg34  38008  cdlemk5u  38157  cdlemk6u  38158  cdlemk21N  38169  cdlemk20  38170  cdlemk26b-3  38201  cdlemk26-3  38202  cdlemk28-3  38204  cdlemky  38222  cdlemk11t  38242  cdlemkyyN  38258  dihmeetlem20N  38622  stoweidlem56  42698