This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ee201

Description: e201 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee201.1	$⊢ φ \to (ψ \to χ)$
	ee201.2	$⊢ θ$
	ee201.3	$⊢ φ \to τ$
	ee201.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	ee201	$⊢ φ \to (ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee201.1	$⊢ φ \to (ψ \to χ)$
2		ee201.2	$⊢ θ$
3		ee201.3	$⊢ φ \to τ$
4		ee201.4	$⊢ χ \to (θ \to (τ \to η))$
5	2	a1i	$⊢ ψ \to θ$
6	5	a1i	$⊢ φ \to (ψ \to θ)$
7	3	a1d	$⊢ φ \to (ψ \to τ)$
8	1 6 7 4	ee222	$⊢ φ \to (ψ \to η)$