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Theorem bothfbothsame 46815
Description: Given both a, b are equivalent to , there exists a proof for a is the same as b. (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
bothfbothsame.1 (𝜑 ↔ ⊥)
bothfbothsame.2 (𝜓 ↔ ⊥)
Assertion
Ref Expression
bothfbothsame (𝜑𝜓)

Proof of Theorem bothfbothsame
StepHypRef Expression
1 bothfbothsame.1 . 2 (𝜑 ↔ ⊥)
2 bothfbothsame.2 . 2 (𝜓 ↔ ⊥)
31, 2bitr4i 278 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wfal 1549
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 207
This theorem is referenced by:  mdandyv0  46864  mdandyv1  46865  mdandyv2  46866  mdandyv3  46867  mdandyv4  46868  mdandyv5  46869  mdandyv6  46870  mdandyv7  46871  mdandyv8  46872  mdandyv9  46873  mdandyv10  46874  mdandyv11  46875  mdandyv12  46876  mdandyv13  46877  mdandyv14  46878  dandysum2p2e4  46913
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