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Metamath Proof Explorer

Theorem ee03

Description: e03 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee03.1	$⊢ φ$
	ee03.2	$⊢ ψ \to (χ \to (θ \to τ))$
	ee03.3	$⊢ φ \to (τ \to η)$
Assertion	ee03	$⊢ ψ \to (χ \to (θ \to η))$

Proof

Step	Hyp	Ref	Expression
1		ee03.1	$⊢ φ$
2		ee03.2	$⊢ ψ \to (χ \to (θ \to τ))$
3		ee03.3	$⊢ φ \to (τ \to η)$
4	1	a1i	$⊢ ψ \to φ$
5	4	a1d	$⊢ ψ \to (χ \to φ)$
6	5	a1dd	$⊢ ψ \to (χ \to (θ \to φ))$
7	6 2 3	ee33	$⊢ ψ \to (χ \to (θ \to η))$