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 FunFAAdomFF''''AranF

Proof

Step Hyp Ref Expression
1 iba FunFAAdomFAdomFFunFA
2 df-dfat FdefAtAAdomFFunFA
3 dfatafv2rnb FdefAtAF''''AranF
4 2 3 bitr3i AdomFFunFAF''''AranF
5 1 4 bitrdi FunFAAdomFF''''AranF