Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > spei | Structured version Visualization version Unicode version |
Description: Inference from existential specialization, using implicit substitution. Remove a distinct variable constraint. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 12-May-2018.) |
Ref | Expression |
---|---|
spei.1 | |
spei.2 |
Ref | Expression |
---|---|
spei |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6e 2250 | . 2 | |
2 | spei.2 | . . 3 | |
3 | spei.1 | . . 3 | |
4 | 2, 3 | mpbiri 248 | . 2 |
5 | 1, 4 | eximii 1764 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: elirrv 8504 bnj1014 31030 |
Copyright terms: Public domain | W3C validator |