Metamath Proof Explorer


Theorem nfttc

Description: Bound-variable hypothesis builder for transitive closure. (Contributed by Matthew House, 6-Apr-2026)

Ref Expression
Hypothesis nfttc.1 ⊢ Ⅎ _ x A
Assertion nfttc Could not format assertion : No typesetting found for |- F/_ x TC+ A with typecode |-

Proof

Step Hyp Ref Expression
1 nfttc.1 ⊢ Ⅎ _ x A
2 df-ttc Could not format TC+ A = U_ y e. A U. ( rec ( ( z e. _V |-> U. z ) , { y } ) " _om ) : No typesetting found for |- TC+ A = U_ y e. A U. ( rec ( ( z e. _V |-> U. z ) , { y } ) " _om ) with typecode |-
3 nfcv ⊢ Ⅎ _ x ⋃ rec ⁡ z ∈ V ⟼ ⋃ z y ω
4 1 3 nfiun ⊢ Ⅎ _ x ⋃ y ∈ A ⋃ rec ⁡ z ∈ V ⟼ ⋃ z y ω
5 2 4 nfcxfr Could not format F/_ x TC+ A : No typesetting found for |- F/_ x TC+ A with typecode |-