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Metamath Proof Explorer

Theorem ee210

Description: e210 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee210.1	$⊢ φ \to (ψ \to χ)$
	ee210.2	$⊢ φ \to θ$
	ee210.3	$⊢ τ$
	ee210.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	ee210	$⊢ φ \to (ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee210.1	$⊢ φ \to (ψ \to χ)$
2		ee210.2	$⊢ φ \to θ$
3		ee210.3	$⊢ τ$
4		ee210.4	$⊢ χ \to (θ \to (τ \to η))$
5	2	a1d	$⊢ φ \to (ψ \to θ)$
6	3	a1i	$⊢ ψ \to τ$
7	6	a1i	$⊢ φ \to (ψ \to τ)$
8	1 5 7 4	ee222	$⊢ φ \to (ψ \to η)$