Theorem simp3r3 1284

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp3r3	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simp3r3

Step	Hyp	Ref	Expression
1		simpr3 1197	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  hash7g  14409  nllyrest  23430  bdayfinbndlem1  28463  cdlemblem  40049  cdleme21  40593  cdleme22b  40597  cdleme40m  40723  cdlemg34  40968  cdlemk5u  41117  cdlemk6u  41118  cdlemk21N  41129  cdlemk20  41130  cdlemk26b-3  41161  cdlemk26-3  41162  cdlemk28-3  41164  cdlemky  41182  cdlemk11t  41202  cdlemkyyN  41218  dihmeetlem20N  41582  stoweidlem56  46296