Theorem simp3r3 1285

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 1198	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1136	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  hash7g  14448  nllyrest  23451  bdayfinbndlem1  28459  cdlemblem  40239  cdleme21  40783  cdleme22b  40787  cdleme40m  40913  cdlemg34  41158  cdlemk5u  41307  cdlemk6u  41308  cdlemk21N  41319  cdlemk20  41320  cdlemk26b-3  41351  cdlemk26-3  41352  cdlemk28-3  41354  cdlemky  41372  cdlemk11t  41392  cdlemkyyN  41408  dihmeetlem20N  41772  stoweidlem56  46484