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Theorem mdandyv11 38419
 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
mdandyv11.1
mdandyv11.2
mdandyv11.3
mdandyv11.4
mdandyv11.5
mdandyv11.6
Assertion
Ref Expression
mdandyv11

Proof of Theorem mdandyv11
StepHypRef Expression
1 mdandyv11.3 . . . . 5
2 mdandyv11.2 . . . . 5
31, 2bothtbothsame 38357 . . . 4
4 mdandyv11.4 . . . . 5
54, 2bothtbothsame 38357 . . . 4
63, 5pm3.2i 456 . . 3
7 mdandyv11.5 . . . 4
8 mdandyv11.1 . . . 4
97, 8bothfbothsame 38358 . . 3
106, 9pm3.2i 456 . 2
11 mdandyv11.6 . . 3
1211, 2bothtbothsame 38357 . 2
1310, 12pm3.2i 456 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   wtru 1438   wfal 1442 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 188  df-an 372 This theorem is referenced by: (None)
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