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Mirrors > Home > MPE Home > Th. List > axext3ALT | Structured version Visualization version Unicode version |
Description: Alternate proof of axext3 2604, shorter but uses more axioms. (Contributed by NM, 15-Sep-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axext3ALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elequ2 2004 | . . . . 5 | |
2 | 1 | bibi1d 333 | . . . 4 |
3 | 2 | albidv 1849 | . . 3 |
4 | equequ1 1952 | . . 3 | |
5 | 3, 4 | imbi12d 334 | . 2 |
6 | ax-ext 2602 | . 2 | |
7 | 5, 6 | chvarv 2263 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 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-9 1999 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: (None) |
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