Theorem simp3l1 1280

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 1193	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑)
2	1	3ad2ant3 1136	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:  bdayfinbndlem1  28459  cvmlift2lem10  35494  cdleme26ee  40806  cdleme36m  40907  cdleme40m  40913  cdlemg18b  41125  cdlemk5u  41307  cdlemk6u  41308  cdlemk21N  41319  cdlemk20  41320  cdlemk27-3  41353  cdlemk28-3  41354  dihmeetlem20N  41772