Theorem simp3l1 1278

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 1191	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

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:  cvmlift2lem10  35280  cdleme26ee  40317  cdleme36m  40418  cdleme40m  40424  cdlemg18b  40636  cdlemk5u  40818  cdlemk6u  40819  cdlemk21N  40830  cdlemk20  40831  cdlemk27-3  40864  cdlemk28-3  40865  dihmeetlem20N  41283