Prove: A & B => C => [A => [B => C]]

	Suppose...

	1	A & B => C
		Premise

		
		Prove: A => [B => C]
		
		Suppose...

		2	A
			Premise

		We have two cases to consider:

		3	B | ~B
			Or Not

			
			Case 1
			------
			
			Prove: B => [B => C]
			
			Suppose...

			4	B
				Premise

				
				Prove: B => C
				
				Suppose...

				5	B
					Premise

				6	A & B
					Join, 2, 4

				7	C
					Detach, 1, 6

			As Required:

			8	B => C
				Conclusion, 5

		Case 1
		------
		
		As Required:

		9	B => [B => C]
			Conclusion, 4

			
			Case 2
			------
			
			Prove: ~B => [B => C]
			
			Suppose...

			10	~B
				Premise

			11	~B | C
				Arb Or, 10

			12	~~B => C
				Imply-Or, 11

			13	B => C
				Rem DNeg, 12

		Case 2
		------
		
		As Required:

		14	~B => [B => C]
			Conclusion, 10

		Joining results for Cases rule...

		15	[B => [B => C]] & [~B => [B => C]]
			Join, 9, 14

		In both cases...

		16	B => C
			Cases, 3, 15

	As Required:

	17	A => [B => C]
		Conclusion, 2

As Required:

18	A & B => C => [A => [B => C]]
	Conclusion, 1