Theorem simp-4r 743

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 735	. 2 ⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → ψ)
2	1	adantr 451	1 ⊢ (((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) → ψ)

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  simp-5r  745