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Theorem mdandyv15 27885
 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.)
Hypotheses
Ref Expression
mdandyv15.1
mdandyv15.2
mdandyv15.3
mdandyv15.4
mdandyv15.5
mdandyv15.6
Assertion
Ref Expression
mdandyv15

Proof of Theorem mdandyv15
StepHypRef Expression
1 mdandyv15.3 . . . . 5
2 mdandyv15.2 . . . . 5
31, 2bothtbothsame 27843 . . . 4
4 mdandyv15.4 . . . . 5
54, 2bothtbothsame 27843 . . . 4
63, 5pm3.2i 442 . . 3
7 mdandyv15.5 . . . 4
87, 2bothtbothsame 27843 . . 3
96, 8pm3.2i 442 . 2
10 mdandyv15.6 . . 3
1110, 2bothtbothsame 27843 . 2
129, 11pm3.2i 442 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wtru 1325   wfal 1326 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 178  df-an 361
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