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Theorem mdandyvr10 27243
 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.)
Hypotheses
Ref Expression
mdandyvr10.1
mdandyvr10.2
mdandyvr10.3
mdandyvr10.4
mdandyvr10.5
mdandyvr10.6
Assertion
Ref Expression
mdandyvr10

Proof of Theorem mdandyvr10
StepHypRef Expression
1 mdandyvr10.3 . . . . 5
2 mdandyvr10.1 . . . . 5
31, 2bitri 240 . . . 4
4 mdandyvr10.4 . . . . 5
5 mdandyvr10.2 . . . . 5
64, 5bitri 240 . . . 4
73, 6pm3.2i 441 . . 3
8 mdandyvr10.5 . . . 4
98, 2bitri 240 . . 3
107, 9pm3.2i 441 . 2
11 mdandyvr10.6 . . 3
1211, 5bitri 240 . 2
1310, 12pm3.2i 441 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360
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