Theorem simp3r2 1283

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 1196	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1136	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

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  22990  cdlemblem  38664  cdleme21  39208  cdleme22b  39212  cdleme40m  39338  cdlemg34  39583  cdlemk5u  39732  cdlemk6u  39733  cdlemk21N  39744  cdlemk20  39745  cdlemk26b-3  39776  cdlemk26-3  39777  cdlemk28-3  39779  cdlemky  39797  cdlemk11t  39817  cdlemkyyN  39833  stoweidlem56  44772