Metamath Proof Explorer
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 |
|- F/_ x A |
|
|
nfbr.2 |
|- F/_ x R |
|
|
nfbr.3 |
|- F/_ x B |
|
Assertion |
nfbr |
|- F/ x A R B |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
nfbr.1 |
|- F/_ x A |
| 2 |
|
nfbr.2 |
|- F/_ x R |
| 3 |
|
nfbr.3 |
|- F/_ x B |
| 4 |
1
|
a1i |
|- ( T. -> F/_ x A ) |
| 5 |
2
|
a1i |
|- ( T. -> F/_ x R ) |
| 6 |
3
|
a1i |
|- ( T. -> F/_ x B ) |
| 7 |
4 5 6
|
nfbrd |
|- ( T. -> F/ x A R B ) |
| 8 |
7
|
mptru |
|- F/ x A R B |