Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > mdandyv1 | Structured version Visualization version Unicode version |
Description: Given the equivalences set in the hypotheses, there exist a proof where ch, th, ta, et match ph, ps accordingly. (Contributed by Jarvin Udandy, 6-Sep-2016.) |
Ref | Expression |
---|---|
mdandyv1.1 | |
mdandyv1.2 | |
mdandyv1.3 | |
mdandyv1.4 | |
mdandyv1.5 | |
mdandyv1.6 |
Ref | Expression |
---|---|
mdandyv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdandyv1.3 | . . . . 5 | |
2 | mdandyv1.2 | . . . . 5 | |
3 | 1, 2 | bothtbothsame 41066 | . . . 4 |
4 | mdandyv1.4 | . . . . 5 | |
5 | mdandyv1.1 | . . . . 5 | |
6 | 4, 5 | bothfbothsame 41067 | . . . 4 |
7 | 3, 6 | pm3.2i 471 | . . 3 |
8 | mdandyv1.5 | . . . 4 | |
9 | 8, 5 | bothfbothsame 41067 | . . 3 |
10 | 7, 9 | pm3.2i 471 | . 2 |
11 | mdandyv1.6 | . . 3 | |
12 | 11, 5 | bothfbothsame 41067 | . 2 |
13 | 10, 12 | pm3.2i 471 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wtru 1484 wfal 1488 |
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: (None) |
Copyright terms: Public domain | W3C validator |