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Mirrors > Home > MPE Home > Th. List > Mathboxes > ifpnannanb | Structured version Visualization version Unicode version |
Description: Factor conditional logic operator over nand in terms 2 and 3. (Contributed by RP, 21-Apr-2020.) |
Ref | Expression |
---|---|
ifpnannanb | if- if- if- |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nan 1448 | . . 3 | |
2 | df-nan 1448 | . . 3 | |
3 | ifpbi23 37817 | . . 3 if- if- | |
4 | 1, 2, 3 | mp2an 708 | . 2 if- if- |
5 | ifpananb 37851 | . . . 4 if- if- if- | |
6 | 5 | notbii 310 | . . 3 if- if- if- |
7 | ifpnotnotb 37824 | . . 3 if- if- | |
8 | df-nan 1448 | . . 3 if- if- if- if- | |
9 | 6, 7, 8 | 3bitr4i 292 | . 2 if- if- if- |
10 | 4, 9 | bitri 264 | 1 if- if- if- |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wa 384 if-wif 1012 wnan 1447 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ifp 1013 df-nan 1448 |
This theorem is referenced by: (None) |
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