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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