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Metamath Proof Explorer

Theorem ee211

Description: e211 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee211.1	$⊢ φ \to (ψ \to χ)$
	ee211.2	$⊢ φ \to θ$
	ee211.3	$⊢ φ \to τ$
	ee211.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	ee211	$⊢ φ \to (ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee211.1	$⊢ φ \to (ψ \to χ)$
2		ee211.2	$⊢ φ \to θ$
3		ee211.3	$⊢ φ \to τ$
4		ee211.4	$⊢ χ \to (θ \to (τ \to η))$
5	2	a1d	$⊢ φ \to (ψ \to θ)$
6	3	a1d	$⊢ φ \to (ψ \to τ)$
7	1 5 6 4	ee222	$⊢ φ \to (ψ \to η)$