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Mirrors > Home > MPE Home > Th. List > nfbr | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for binary relation. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
nfbr.1 | ⊢ Ⅎ𝑥𝐴 |
nfbr.2 | ⊢ Ⅎ𝑥𝑅 |
nfbr.3 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfbr | ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfbr.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
3 | nfbr.2 | . . . 4 ⊢ Ⅎ𝑥𝑅 | |
4 | 3 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝑅) |
5 | nfbr.3 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
6 | 5 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐵) |
7 | 2, 4, 6 | nfbrd 5108 | . 2 ⊢ (⊤ → Ⅎ𝑥 𝐴𝑅𝐵) |
8 | 7 | mptru 1550 | 1 ⊢ Ⅎ𝑥 𝐴𝑅𝐵 |
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