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Metamath Proof Explorer

Theorem nfbr

Description: Bound-variable hypothesis builder for binary relation. (Contributed by NM, 1-Sep-1999) (Revised by Mario Carneiro, 14-Oct-2016)

Ref Expression
Hypotheses nfbr.1 ⊢ Ⅎ _ x A
nfbr.2 ⊢ Ⅎ _ x R
nfbr.3 ⊢ Ⅎ _ x B
Assertion nfbr ⊢ Ⅎ x A R B

Proof

Step Hyp Ref Expression
1 nfbr.1 ⊢ Ⅎ _ x A
2 nfbr.2 ⊢ Ⅎ _ x R
3 nfbr.3 ⊢ Ⅎ _ x B
4 1 a1i ⊢ ⊤ → Ⅎ _ x A
5 2 a1i ⊢ ⊤ → Ⅎ _ x R
6 3 a1i ⊢ ⊤ → Ⅎ _ x B
7 4 5 6 nfbrd ⊢ ⊤ → Ⅎ x A R B
8 7 mptru ⊢ Ⅎ x A R B