MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rbaibd Structured version   Visualization version   GIF version

Theorem rbaibd 541
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.)
Hypothesis
Ref Expression
baibd.1 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
Assertion
Ref Expression
rbaibd ((𝜑𝜃) → (𝜓𝜒))

Proof of Theorem rbaibd
StepHypRef Expression
1 baibd.1 . . 3 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
21biancomd 464 . 2 (𝜑 → (𝜓 ↔ (𝜃𝜒)))
32baibd 540 1 ((𝜑𝜃) → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396
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 206  df-an 397
This theorem is referenced by:  qsqueeze  12934  o1lo12  15245  incexc2  15548  gexdvds  19187  fsumvma  26359  qusker  31545
  Copyright terms: Public domain W3C validator