Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > mdandyvr3 | Structured version Visualization version Unicode version |
Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.) |
Ref | Expression |
---|---|
mdandyvr3.1 | |
mdandyvr3.2 | |
mdandyvr3.3 | |
mdandyvr3.4 | |
mdandyvr3.5 | |
mdandyvr3.6 |
Ref | Expression |
---|---|
mdandyvr3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdandyvr3.3 | . . . . 5 | |
2 | mdandyvr3.2 | . . . . 5 | |
3 | 1, 2 | bitri 264 | . . . 4 |
4 | mdandyvr3.4 | . . . . 5 | |
5 | 4, 2 | bitri 264 | . . . 4 |
6 | 3, 5 | pm3.2i 471 | . . 3 |
7 | mdandyvr3.5 | . . . 4 | |
8 | mdandyvr3.1 | . . . 4 | |
9 | 7, 8 | bitri 264 | . . 3 |
10 | 6, 9 | pm3.2i 471 | . 2 |
11 | mdandyvr3.6 | . . 3 | |
12 | 11, 8 | bitri 264 | . 2 |
13 | 10, 12 | pm3.2i 471 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 |
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-an 386 |
This theorem is referenced by: mdandyvr12 41144 |
Copyright terms: Public domain | W3C validator |