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 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  14525  nllyrest  23494  cdlemblem  39795  cdleme21  40339  cdleme22b  40343  cdleme40m  40469  cdlemg34  40714  cdlemk5u  40863  cdlemk6u  40864  cdlemk21N  40875  cdlemk20  40876  cdlemk26b-3  40907  cdlemk26-3  40908  cdlemk28-3  40910  cdlemky  40928  cdlemk11t  40948  cdlemkyyN  40964  dihmeetlem20N  41328  stoweidlem56  46071