Metamath Proof Explorer


Theorem isfsuppd

Description: Deduction form of isfsupp . (Contributed by SN, 29-Jul-2024)

Ref Expression
Hypotheses isfsuppd.r φ R V
isfsuppd.z φ Z W
isfsuppd.1 φ Fun R
isfsuppd.2 φ R supp Z Fin
Assertion isfsuppd φ finSupp Z R

Proof

Step Hyp Ref Expression
1 isfsuppd.r φ R V
2 isfsuppd.z φ Z W
3 isfsuppd.1 φ Fun R
4 isfsuppd.2 φ R supp Z Fin
5 isfsupp R V Z W finSupp Z R Fun R R supp Z Fin
6 1 2 5 syl2anc φ finSupp Z R Fun R R supp Z Fin
7 3 4 6 mpbir2and φ finSupp Z R