Theorem simp3r2 1262

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 1175	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1115	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 387   ∧ w3a 1068

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 388  df-3an 1070

This theorem is referenced by:  nllyrest  21798  cdlemblem  36380  cdleme21  36924  cdleme22b  36928  cdleme40m  37054  cdlemg34  37299  cdlemk5u  37448  cdlemk6u  37449  cdlemk21N  37460  cdlemk20  37461  cdlemk26b-3  37492  cdlemk26-3  37493  cdlemk28-3  37495  cdlemky  37513  cdlemk11t  37533  cdlemkyyN  37549  stoweidlem56  41778