Metamath Proof Explorer

Theorem ee323

Description: e323 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee323.1	$⊢ φ \to (ψ \to (χ \to θ))$
	ee323.2	$⊢ φ \to (ψ \to τ)$
	ee323.3	$⊢ φ \to (ψ \to (χ \to η))$
	ee323.4	$⊢ θ \to (τ \to (η \to ζ))$
Assertion	ee323	$⊢ φ \to (ψ \to (χ \to ζ))$

Proof

Step	Hyp	Ref	Expression
1		ee323.1	$⊢ φ \to (ψ \to (χ \to θ))$
2		ee323.2	$⊢ φ \to (ψ \to τ)$
3		ee323.3	$⊢ φ \to (ψ \to (χ \to η))$
4		ee323.4	$⊢ θ \to (τ \to (η \to ζ))$
5	2	a1dd	$⊢ φ \to (ψ \to (χ \to τ))$
6	1 5 3 4	ee333	$⊢ φ \to (ψ \to (χ \to ζ))$