Theorem simp-4r 510

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
simp-4r	⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Proof of Theorem simp-4r

Step	Hyp	Ref	Expression
1		simpllr 502	. 2 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	adantr 271	1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  simp-5r  512  fimax2gtri  6671  finexdc  6672  exmidfodomrlemr  6889  exmidfodomrlemrALT  6890  supinfneg  9144  infsupneg  9145  hashunlem  10273  sumeq2  10809  fsumconst  10909