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

Metamath Proof Explorer

Theorem ee221

Description: e221 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee221.1	$⊢ φ \to (ψ \to χ)$
	ee221.2	$⊢ φ \to (ψ \to θ)$
	ee221.3	$⊢ φ \to τ$
	ee221.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	ee221	$⊢ φ \to (ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee221.1	$⊢ φ \to (ψ \to χ)$
2		ee221.2	$⊢ φ \to (ψ \to θ)$
3		ee221.3	$⊢ φ \to τ$
4		ee221.4	$⊢ χ \to (θ \to (τ \to η))$
5	3	a1d	$⊢ φ \to (ψ \to τ)$
6	1 2 5 4	ee222	$⊢ φ \to (ψ \to η)$