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Mirrors > Home > MPE Home > Th. List > dtrucor | Structured version Visualization version Unicode version |
Description: Corollary of dtru 4857. This example illustrates the danger of blindly trusting the standard Deduction Theorem without accounting for free variables: the theorem form of this deduction is not valid, as shown by dtrucor2 4901. (Contributed by NM, 27-Jun-2002.) |
Ref | Expression |
---|---|
dtrucor.1 |
Ref | Expression |
---|---|
dtrucor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dtru 4857 | . . 3 | |
2 | 1 | pm2.21i 116 | . 2 |
3 | dtrucor.1 | . 2 | |
4 | 2, 3 | mpg 1724 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wal 1481 wne 2794 |
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 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-nul 4789 ax-pow 4843 |
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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