Description: The same as ex-natded5.2 and ex-natded5.2-2 but with no context. (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ex-natded5.2i.1 | |- ( ( ps /\ ch ) -> th ) |
|
| ex-natded5.2i.2 | |- ( ch -> ps ) |
||
| ex-natded5.2i.3 | |- ch |
||
| Assertion | ex-natded5.2i | |- th |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ex-natded5.2i.1 | |- ( ( ps /\ ch ) -> th ) |
|
| 2 | ex-natded5.2i.2 | |- ( ch -> ps ) |
|
| 3 | ex-natded5.2i.3 | |- ch |
|
| 4 | 3 2 | ax-mp | |- ps |
| 5 | 4 3 | pm3.2i | |- ( ps /\ ch ) |
| 6 | 5 1 | ax-mp | |- th |