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	|- ( ph -> ps )
	ee120.2	|- ( ph -> ( ch -> th ) )
	ee120.3	|- ta
	ee120.4	|- ( ps -> ( th -> ( ta -> et ) ) )
Assertion	ee120	|- ( ph -> ( ch -> et ) )

Proof

Step	Hyp	Ref	Expression
1		ee120.1	|- ( ph -> ps )
2		ee120.2	|- ( ph -> ( ch -> th ) )
3		ee120.3	|- ta
4		ee120.4	|- ( ps -> ( th -> ( ta -> et ) ) )
5	1	a1d	|- ( ph -> ( ch -> ps ) )
6	3	a1i	|- ( ch -> ta )
7	6	a1i	|- ( ph -> ( ch -> ta ) )
8	5 2 7 4	ee222	|- ( ph -> ( ch -> et ) )