Metamath Proof Explorer


Theorem fsnd

Description: A singleton of an ordered pair is a function. (Contributed by AV, 17-Apr-2021)

Ref Expression
Hypotheses fsnd.a φAV
fsnd.b φBW
Assertion fsnd φAB:AW

Proof

Step Hyp Ref Expression
1 fsnd.a φAV
2 fsnd.b φBW
3 1 2 jca φAVBW
4 f1sng AVBWAB:A1-1W
5 f1f AB:A1-1WAB:AW
6 3 4 5 3syl φAB:AW