Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > 19.38b | Structured version Visualization version Unicode version |
Description: Under a non-freeness hypothesis, the implication 19.38 1766 can be strengthened to an equivalence. See also 19.38a 1767. (Contributed by BJ, 3-Nov-2021.) |
Ref | Expression |
---|---|
19.38b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.38 1766 | . 2 | |
2 | df-nf 1710 | . . 3 | |
3 | exim 1761 | . . . 4 | |
4 | imim2 58 | . . . 4 | |
5 | 3, 4 | syl5 34 | . . 3 |
6 | 2, 5 | sylbi 207 | . 2 |
7 | 1, 6 | impbid2 216 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wex 1704 wnf 1708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |