Theorem simp3r3 1284

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 1197	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1136	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 397   ∧ w3a 1088

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 398  df-3an 1090

This theorem is referenced by:  nllyrest  22959  cdlemblem  38570  cdleme21  39114  cdleme22b  39118  cdleme40m  39244  cdlemg34  39489  cdlemk5u  39638  cdlemk6u  39639  cdlemk21N  39650  cdlemk20  39651  cdlemk26b-3  39682  cdlemk26-3  39683  cdlemk28-3  39685  cdlemky  39703  cdlemk11t  39723  cdlemkyyN  39739  dihmeetlem20N  40103  stoweidlem56  44645