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Metamath Proof Explorer

Theorem ee31

Description: e31 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee31.1	$⊢ φ \to (ψ \to (χ \to θ))$
	ee31.2	$⊢ φ \to τ$
	ee31.3	$⊢ θ \to (τ \to η)$
Assertion	ee31	$⊢ φ \to (ψ \to (χ \to η))$

Proof

Step	Hyp	Ref	Expression
1		ee31.1	$⊢ φ \to (ψ \to (χ \to θ))$
2		ee31.2	$⊢ φ \to τ$
3		ee31.3	$⊢ θ \to (τ \to η)$
4	2	a1d	$⊢ φ \to (χ \to τ)$
5	4	a1d	$⊢ φ \to (ψ \to (χ \to τ))$
6	1 5 3	ee33	$⊢ φ \to (ψ \to (χ \to η))$