Theorem simp3r2 1281

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 1194	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1134	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 396  df-3an 1088

This theorem is referenced by:  nllyrest  23311  cdlemblem  39131  cdleme21  39675  cdleme22b  39679  cdleme40m  39805  cdlemg34  40050  cdlemk5u  40199  cdlemk6u  40200  cdlemk21N  40211  cdlemk20  40212  cdlemk26b-3  40243  cdlemk26-3  40244  cdlemk28-3  40246  cdlemky  40264  cdlemk11t  40284  cdlemkyyN  40300  stoweidlem56  45234