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Metamath Proof Explorer

Theorem ee022

Description: e022 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee022.1	$⊢ φ$
	ee022.2	$⊢ ψ \to (χ \to θ)$
	ee022.3	$⊢ ψ \to (χ \to τ)$
	ee022.4	$⊢ φ \to (θ \to (τ \to η))$
Assertion	ee022	$⊢ ψ \to (χ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee022.1	$⊢ φ$
2		ee022.2	$⊢ ψ \to (χ \to θ)$
3		ee022.3	$⊢ ψ \to (χ \to τ)$
4		ee022.4	$⊢ φ \to (θ \to (τ \to η))$
5	1	a1i	$⊢ χ \to φ$
6	5	a1i	$⊢ ψ \to (χ \to φ)$
7	6 2 3 4	ee222	$⊢ ψ \to (χ \to η)$