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Mirrors > Home > MPE Home > Th. List > axc16g | Structured version Visualization version Unicode version |
Description: Generalization of axc16 2135. Use the latter when sufficient. This proof only requires, on top of { ax-1 6-- ax-7 1935 }, theorem ax12v 2048. (Contributed by NM, 15-May-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 18-Feb-2018.) Remove dependency on ax-13 2246, along an idea of BJ. (Revised by Wolf Lammen, 30-Nov-2019.) (Revised by BJ, 7-Jul-2021.) Shorten axc11rv 2139. (Revised by Wolf Lammen, 11-Oct-2021.) |
Ref | Expression |
---|---|
axc16g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aevlem 1981 | . 2 | |
2 | ax12v 2048 | . . . 4 | |
3 | 2 | sps 2055 | . . 3 |
4 | pm2.27 42 | . . . 4 | |
5 | 4 | al2imi 1743 | . . 3 |
6 | 3, 5 | syld 47 | . 2 |
7 | 1, 6 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: 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-12 2047 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: axc16 2135 axc16gb 2136 axc16nf 2137 axc11v 2138 axc11rv 2139 aevOLD 2162 axc16nfALT 2323 |
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