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Theorem mpbir3and 1135
Description: Detach a conjunction of truths in a biconditional. (Contributed by Mario Carneiro, 11-May-2014.) (Revised by Mario Carneiro, 9-Jan-2015.)
Hypotheses
Ref Expression
mpbir3and.1
mpbir3and.2
mpbir3and.3
mpbir3and.4
Assertion
Ref Expression
mpbir3and

Proof of Theorem mpbir3and
StepHypRef Expression
1 mpbir3and.1 . . 3
2 mpbir3and.2 . . 3
3 mpbir3and.3 . . 3
41, 2, 33jca 1132 . 2
5 mpbir3and.4 . 2
64, 5mpbird 223 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  spaccl  6286
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