Metamath Proof Explorer


Theorem dmafv2rnb

Description: The alternate function value at a class A is defined, i.e., in the range of the function, iff A is in the domain of the function. (Contributed by AV, 3-Sep-2022)

Ref Expression
Assertion dmafv2rnb Fun F A A dom F F '''' A ran F

Proof

Step Hyp Ref Expression
1 iba Fun F A A dom F A dom F Fun F A
2 df-dfat F defAt A A dom F Fun F A
3 dfatafv2rnb F defAt A F '''' A ran F
4 2 3 bitr3i A dom F Fun F A F '''' A ran F
5 1 4 bitrdi Fun F A A dom F F '''' A ran F