Theorem simp3l1 1297

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

Assertion

Ref	Expression
simp3l1	⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Proof of Theorem simp3l1

Step	Hyp	Ref	Expression
1		simpl1 1210	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant3 1153	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 1105

This theorem is referenced by:  bdayfinbndlem1  28638  cvmlift2lem10  35782  cdleme26ee  41112  cdleme36m  41213  cdleme40m  41219  cdlemg18b  41431  cdlemk5u  41613  cdlemk6u  41614  cdlemk21N  41625  cdlemk20  41626  cdlemk27-3  41659  cdlemk28-3  41660  dihmeetlem20N  42078