Theorem simp3r2 1295

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 1208	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1147	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 400  df-3an 1099

This theorem is referenced by:  nllyrest  23533  bdayfinbndlem1  28547  cdlemblem  40377  cdleme21  40921  cdleme22b  40925  cdleme40m  41051  cdlemg34  41296  cdlemk5u  41445  cdlemk6u  41446  cdlemk21N  41457  cdlemk20  41458  cdlemk26b-3  41489  cdlemk26-3  41490  cdlemk28-3  41492  cdlemky  41510  cdlemk11t  41530  cdlemkyyN  41546  stoweidlem56  46590