Mathbox for Andrew Salmon |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5c4c711 | Structured version Visualization version Unicode version |
Description: Proof of a theorem that can act as a sole axiom for pure predicate calculus with ax-gen 1722 as the inference rule. This proof extends the idea of axc5c711 34203 and related theorems. (Contributed by Andrew Salmon, 14-Jul-2011.) |
Ref | Expression |
---|---|
axc5c4c711 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc4 2130 | . . 3 | |
2 | hbn1 2020 | . . . . 5 | |
3 | axc7 2132 | . . . . . 6 | |
4 | 3 | con1i 144 | . . . . 5 |
5 | 2, 4 | alrimih 1751 | . . . 4 |
6 | ax-11 2034 | . . . 4 | |
7 | 5, 6 | syl 17 | . . 3 |
8 | 1, 7 | nsyl4 156 | . 2 |
9 | pm2.21 120 | . . . 4 | |
10 | 9 | spsd 2057 | . . 3 |
11 | 10, 1 | ja 173 | . 2 |
12 | 8, 11 | ja 173 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wal 1481 |
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-10 2019 ax-11 2034 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 |
This theorem is referenced by: axc5c4c711toc5 38603 axc5c4c711toc4 38604 axc5c4c711toc7 38605 axc5c4c711to11 38606 |
Copyright terms: Public domain | W3C validator |