Metamath Proof Explorer


Theorem sub4d

Description: Rearrangement of 4 terms in a subtraction. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses negidd.1 φ A
pncand.2 φ B
subaddd.3 φ C
addsub4d.4 φ D
Assertion sub4d φ A - B - C D = A - C - B D

Proof

Step Hyp Ref Expression
1 negidd.1 φ A
2 pncand.2 φ B
3 subaddd.3 φ C
4 addsub4d.4 φ D
5 sub4 A B C D A - B - C D = A - C - B D
6 1 2 3 4 5 syl22anc φ A - B - C D = A - C - B D