Metamath Proof Explorer


Theorem recdiv2d

Description: Division into a reciprocal. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses div1d.1 φA
divcld.2 φB
divne0d.3 φA0
divne0d.4 φB0
Assertion recdiv2d φ1AB=1AB

Proof

Step Hyp Ref Expression
1 div1d.1 φA
2 divcld.2 φB
3 divne0d.3 φA0
4 divne0d.4 φB0
5 recdiv2 AA0BB01AB=1AB
6 1 3 2 4 5 syl22anc φ1AB=1AB