This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nfpr

Description: Bound-variable hypothesis builder for unordered pairs. (Contributed by NM, 14-Nov-1995)

Ref Expression
Hypotheses nfpr.1 ⊢ Ⅎ _ x A
nfpr.2 ⊢ Ⅎ _ x B
Assertion nfpr ⊢ Ⅎ _ x A B

Proof

Step Hyp Ref Expression
1 nfpr.1 ⊢ Ⅎ _ x A
2 nfpr.2 ⊢ Ⅎ _ x B
3 dfpr2 ⊢ A B = y | y = A ∨ y = B
4 1 nfeq2 ⊢ Ⅎ x y = A
5 2 nfeq2 ⊢ Ⅎ x y = B
6 4 5 nfor ⊢ Ⅎ x y = A ∨ y = B
7 6 nfab ⊢ Ⅎ _ x y | y = A ∨ y = B
8 3 7 nfcxfr ⊢ Ⅎ _ x A B