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Metamath Proof Explorer

Theorem ee102

Description: e102 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee102.1	$⊢ φ \to ψ$
	ee102.2	$⊢ χ$
	ee102.3	$⊢ φ \to (θ \to τ)$
	ee102.4	$⊢ ψ \to (χ \to (τ \to η))$
Assertion	ee102	$⊢ φ \to (θ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee102.1	$⊢ φ \to ψ$
2		ee102.2	$⊢ χ$
3		ee102.3	$⊢ φ \to (θ \to τ)$
4		ee102.4	$⊢ ψ \to (χ \to (τ \to η))$
5	1	a1d	$⊢ φ \to (θ \to ψ)$
6	2	a1i	$⊢ θ \to χ$
7	6	a1i	$⊢ φ \to (θ \to χ)$
8	5 7 3 4	ee222	$⊢ φ \to (θ \to η)$