Theorem simp1r3 1269

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

Assertion

Ref	Expression
simp1r3	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Proof of Theorem simp1r3

Step	Hyp	Ref	Expression
1		simpr3 1194	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant1 1131	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  lshpkrlem6  37056  atbtwnexOLDN  37388  atbtwnex  37389  3dim3  37410  3atlem5  37428  lplnle  37481  4atlem11  37550  4atexlem7  38016  cdleme22b  38282  stoweidlem60  43491