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Mirrors > Home > MPE Home > Th. List > ax13ALT | Structured version Visualization version Unicode version |
Description: Alternate proof of ax13 2249 from FOL, sp 2053, and axc9 2302. (Contributed by NM, 21-Dec-2015.) (Proof shortened by Wolf Lammen, 31-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax13ALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 2053 | . . . 4 | |
2 | 1 | con3i 150 | . . 3 |
3 | sp 2053 | . . . 4 | |
4 | 3 | con3i 150 | . . 3 |
5 | axc9 2302 | . . 3 | |
6 | 2, 4, 5 | syl2im 40 | . 2 |
7 | ax13b 1964 | . 2 | |
8 | 6, 7 | mpbir 221 | 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-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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