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Theorem mpbir3an 1086
 Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 16-Sep-2011.) (Revised by NM, 9-Jan-2015.)
Hypotheses
Ref Expression
mpbir3an.1
mpbir3an.2
mpbir3an.3
mpbir3an.4
Assertion
Ref Expression
mpbir3an

Proof of Theorem mpbir3an
StepHypRef Expression
1 mpbir3an.1 . . 3
2 mpbir3an.2 . . 3
3 mpbir3an.3 . . 3
41, 2, 33pm3.2i 1082 . 2
5 mpbir3an.4 . 2
64, 5mpbir 134 1
 Colors of variables: wff set class Syntax hints:   wb 98   w3a 885 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110  df-3an 887 This theorem is referenced by:  limon  4239  limom  4336  issmo  5903  1eluzge0  8516  2eluzge0OLD  8518  2eluzge1  8519  0elunit  8854  1elunit  8855  4fvwrd4  8997  fzo0to42pr  9076  resqrexlemga  9621
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