Description: Bound-variable hypothesis builder for substitution into a class. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfcsbw when possible. (Contributed by Mario Carneiro, 12-Oct-2016) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfcsb.1 | |- F/_ x A |
|
| nfcsb.2 | |- F/_ x B |
||
| Assertion | nfcsb | |- F/_ x [_ A / y ]_ B |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfcsb.1 | |- F/_ x A |
|
| 2 | nfcsb.2 | |- F/_ x B |
|
| 3 | nftru | |- F/ y T. |
|
| 4 | 1 | a1i | |- ( T. -> F/_ x A ) |
| 5 | 2 | a1i | |- ( T. -> F/_ x B ) |
| 6 | 3 4 5 | nfcsbd | |- ( T. -> F/_ x [_ A / y ]_ B ) |
| 7 | 6 | mptru | |- F/_ x [_ A / y ]_ B |