Theorem simp3r2 1280

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 1193	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1133	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 1087

This theorem is referenced by:  nllyrest  22618  cdlemblem  37786  cdleme21  38330  cdleme22b  38334  cdleme40m  38460  cdlemg34  38705  cdlemk5u  38854  cdlemk6u  38855  cdlemk21N  38866  cdlemk20  38867  cdlemk26b-3  38898  cdlemk26-3  38899  cdlemk28-3  38901  cdlemky  38919  cdlemk11t  38939  cdlemkyyN  38955  stoweidlem56  43551