Theorem int3

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 is 3expia . (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	int3.1	|- (. (. ph ,. ps ,. ch ). ->. th ).
Assertion	int3	|- (. (. ph ,. ps ). ->. ( ch -> th ) ).

Proof

Step	Hyp	Ref	Expression
1		int3.1	|- (. (. ph ,. ps ,. ch ). ->. th ).
2	1	dfvd3ani	|- ( ( ph /\ ps /\ ch ) -> th )
3	2	3expia	|- ( ( ph /\ ps ) -> ( ch -> th ) )
4	3	dfvd2anir	|- (. (. ph ,. ps ). ->. ( ch -> th ) ).