Theorem simp3r3 1383

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 1253	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1166	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 385   ∧ w3a 1108

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 199  df-an 386  df-3an 1110

This theorem is referenced by:  nllyrest  21618  cdlemblem  35814  cdleme21  36358  cdleme22b  36362  cdleme40m  36488  cdlemg34  36733  cdlemk5u  36882  cdlemk6u  36883  cdlemk21N  36894  cdlemk20  36895  cdlemk26b-3  36926  cdlemk26-3  36927  cdlemk28-3  36929  cdlemky  36947  cdlemk11t  36967  cdlemkyyN  36983  dihmeetlem20N  37347  stoweidlem56  41012