Theorem simp3r2 1278

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

Assertion

Ref	Expression
simp3r2	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Proof of Theorem simp3r2

Step	Hyp	Ref	Expression
1		simpr2 1191	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1131	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  nllyrest  22088  cdlemblem  36923  cdleme21  37467  cdleme22b  37471  cdleme40m  37597  cdlemg34  37842  cdlemk5u  37991  cdlemk6u  37992  cdlemk21N  38003  cdlemk20  38004  cdlemk26b-3  38035  cdlemk26-3  38036  cdlemk28-3  38038  cdlemky  38056  cdlemk11t  38076  cdlemkyyN  38092  stoweidlem56  42334