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Metamath Proof Explorer

Theorem ee212

Description: e212 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee212.1	$⊢ φ \to (ψ \to χ)$
	ee212.2	$⊢ φ \to θ$
	ee212.3	$⊢ φ \to (ψ \to τ)$
	ee212.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	ee212	$⊢ φ \to (ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee212.1	$⊢ φ \to (ψ \to χ)$
2		ee212.2	$⊢ φ \to θ$
3		ee212.3	$⊢ φ \to (ψ \to τ)$
4		ee212.4	$⊢ χ \to (θ \to (τ \to η))$
5	2	a1d	$⊢ φ \to (ψ \to θ)$
6	1 5 3 4	ee222	$⊢ φ \to (ψ \to η)$