Theorem rabtru

Description: Abstract builder using the constant wff T. . (Contributed by Thierry Arnoux, 4-May-2020)

	Ref	Expression
Hypothesis	rabtru.1	|- F/_ x A
Assertion	rabtru	|- { x e. A | T. } = A

Proof

Step	Hyp	Ref	Expression
1		rabtru.1	|- F/_ x A
2		tru	|- T.
3		nfcv	|- F/_ x y
4		nftru	|- F/ x T.
5		biidd	|- ( x = y -> ( T. <-> T. ) )
6	3 1 4 5	elrabf	|- ( y e. { x e. A | T. } <-> ( y e. A /\ T. ) )
7	2 6	mpbiran2	|- ( y e. { x e. A | T. } <-> y e. A )
8	7	eqriv	|- { x e. A | T. } = A