Metamath Proof Explorer

Theorem cnlnadjlem1

Description: Lemma for cnlnadji (Theorem 3.10 of Beran p. 104: every continuous linear operator has an adjoint). The value of the auxiliary functional G . (Contributed by NM, 16-Feb-2006) (New usage is discouraged.)

Ref Expression
Hypotheses cnlnadjlem.1 T LinOp
cnlnadjlem.2 T ContOp
cnlnadjlem.3 G = g T g ih y
Assertion cnlnadjlem1 A G A = T A ih y


Step Hyp Ref Expression
1 cnlnadjlem.1 T LinOp
2 cnlnadjlem.2 T ContOp
3 cnlnadjlem.3 G = g T g ih y
4 fveq2 g = A T g = T A
5 4 oveq1d g = A T g ih y = T A ih y
6 ovex T A ih y V
7 5 3 6 fvmpt A G A = T A ih y