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 φA
pncand.2 φB
subaddd.3 φC
addsub4d.4 φD
Assertion sub4d φA-B-CD=A-C-BD

Proof

Step Hyp Ref Expression
1 negidd.1 φA
2 pncand.2 φB
3 subaddd.3 φC
4 addsub4d.4 φD
5 sub4 ABCDA-B-CD=A-C-BD
6 1 2 3 4 5 syl22anc φA-B-CD=A-C-BD