Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > ax8 | Structured version Visualization version Unicode version |
Description: Proof of ax-8 1992 from ax8v1 1994 and ax8v2 1995, proving sufficiency of the conjunction of the latter two weakened versions of ax8v 1993, which is itself a weakened version of ax-8 1992. (Contributed by BJ, 7-Dec-2020.) (Proof shortened by Wolf Lammen, 11-Apr-2021.) |
Ref | Expression |
---|---|
ax8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equvinv 1959 | . 2 | |
2 | ax8v2 1995 | . . . . 5 | |
3 | 2 | equcoms 1947 | . . . 4 |
4 | ax8v1 1994 | . . . 4 | |
5 | 3, 4 | sylan9 689 | . . 3 |
6 | 5 | exlimiv 1858 | . 2 |
7 | 1, 6 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 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-8 1992 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: elequ1 1997 el 4847 axextdfeq 31703 ax8dfeq 31704 exnel 31708 bj-ax89 32667 bj-el 32796 |
Copyright terms: Public domain | W3C validator |