Theorem simp3r3 1300

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 1213	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1151	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  hash7g  14513  nllyrest  23604  bdayfinbndlem1  28618  cdlemblem  40429  cdleme21  40973  cdleme22b  40977  cdleme40m  41103  cdlemg34  41348  cdlemk5u  41497  cdlemk6u  41498  cdlemk21N  41509  cdlemk20  41510  cdlemk26b-3  41541  cdlemk26-3  41542  cdlemk28-3  41544  cdlemky  41562  cdlemk11t  41582  cdlemkyyN  41598  dihmeetlem20N  41962  stoweidlem56  46628