Users' Mathboxes Mathbox for Jarvin Udandy < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bothtbothsame Structured version   Visualization version   GIF version

Theorem bothtbothsame 46814
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
bothtbothsame.1 (𝜑 ↔ ⊤)
bothtbothsame.2 (𝜓 ↔ ⊤)
Assertion
Ref Expression
bothtbothsame (𝜑𝜓)

Proof of Theorem bothtbothsame
StepHypRef Expression
1 bothtbothsame.1 . 2 (𝜑 ↔ ⊤)
2 bothtbothsame.2 . 2 (𝜓 ↔ ⊤)
31, 2bitr4i 278 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wtru 1538
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:  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  mdandyv15  46879  dandysum2p2e4  46913
  Copyright terms: Public domain W3C validator