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Metamath Proof Explorer

Theorem ee120

Description: Virtual deduction rule e120 without virtual deduction symbols. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee120.1	$⊢ φ \to ψ$
	ee120.2	$⊢ φ \to (χ \to θ)$
	ee120.3	$⊢ τ$
	ee120.4	$⊢ ψ \to (θ \to (τ \to η))$
Assertion	ee120	$⊢ φ \to (χ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee120.1	$⊢ φ \to ψ$
2		ee120.2	$⊢ φ \to (χ \to θ)$
3		ee120.3	$⊢ τ$
4		ee120.4	$⊢ ψ \to (θ \to (τ \to η))$
5	1	a1d	$⊢ φ \to (χ \to ψ)$
6	3	a1i	$⊢ χ \to τ$
7	6	a1i	$⊢ φ \to (χ \to τ)$
8	5 2 7 4	ee222	$⊢ φ \to (χ \to η)$