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Theorem mpbiran2d 708
Description: Detach truth from conjunction in biconditional. Deduction form. (Contributed by Peter Mazsa, 24-Sep-2022.)
Hypotheses
Ref Expression
mpbiran2d.1 (𝜑𝜃)
mpbiran2d.2 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
Assertion
Ref Expression
mpbiran2d (𝜑 → (𝜓𝜒))

Proof of Theorem mpbiran2d
StepHypRef Expression
1 mpbiran2d.1 . 2 (𝜑𝜃)
2 mpbiran2d.2 . . 3 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
32biancomd 463 . 2 (𝜑 → (𝜓 ↔ (𝜃𝜒)))
41, 3mpbirand 707 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wa 395
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  df-an 396
This theorem is referenced by:  opelidres  6012  funsnfsupp  9430  discld  23113  cncfcdm  24938  itgfsum  25877  dchreq  27317  lgsneg  27380  lgsquadlem2  27440  dfconngr1  30217  cover2  37702  iscnrm3rlem6  48742  thincmon  48834  thincepi  48835
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