Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > r19.36v | Structured version Visualization version Unicode version |
Description: Restricted quantifier version of one direction of 19.36 2098. (The other direction holds iff is nonempty, see r19.36zv 4072.) (Contributed by NM, 22-Oct-2003.) |
Ref | Expression |
---|---|
r19.36v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.35 3084 | . 2 | |
2 | id 22 | . . . 4 | |
3 | 2 | rexlimivw 3029 | . . 3 |
4 | 3 | imim2i 16 | . 2 |
5 | 1, 4 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wral 2912 wrex 2913 |
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 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-ral 2917 df-rex 2918 |
This theorem is referenced by: iinss 4571 uniimadom 9366 hashgt12el 13210 |
Copyright terms: Public domain | W3C validator |