Metamath Proof Explorer


Theorem elefmndbas2

Description: Two ways of saying a function is a mapping of A to itself. (Contributed by AV, 27-Jan-2024) (Proof shortened by AV, 29-Mar-2024)

Ref Expression
Hypotheses efmndbas.g No typesetting found for |- G = ( EndoFMnd ` A ) with typecode |-
efmndbas.b B = Base G
Assertion elefmndbas2 F V F B F : A A

Proof

Step Hyp Ref Expression
1 efmndbas.g Could not format G = ( EndoFMnd ` A ) : No typesetting found for |- G = ( EndoFMnd ` A ) with typecode |-
2 efmndbas.b B = Base G
3 1 2 efmndbasabf B = f | f : A A
4 3 a1i F V B = f | f : A A
5 4 eleq2d F V F B F f | f : A A
6 feq1 f = F f : A A F : A A
7 eqid f | f : A A = f | f : A A
8 6 7 elab2g F V F f | f : A A F : A A
9 5 8 bitrd F V F B F : A A