Theorem simp3l1 1378

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 1243	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant3 1166	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 385   ∧ w3a 1108

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 199  df-an 386  df-3an 1110

This theorem is referenced by:  cvmlift2lem10  31803  cdleme26ee  36373  cdleme36m  36474  cdleme40m  36480  cdlemg18b  36692  cdlemk5u  36874  cdlemk6u  36875  cdlemk21N  36886  cdlemk20  36887  cdlemk27-3  36920  cdlemk28-3  36921  dihmeetlem20N  37339