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 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

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:  nllyrest  23430  bdayfinbndlem1  28463  cdlemblem  40053  cdleme21  40597  cdleme22b  40601  cdleme40m  40727  cdlemg34  40972  cdlemk5u  41121  cdlemk6u  41122  cdlemk21N  41133  cdlemk20  41134  cdlemk26b-3  41165  cdlemk26-3  41166  cdlemk28-3  41168  cdlemky  41186  cdlemk11t  41206  cdlemkyyN  41222  stoweidlem56  46300