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Theorem 3anbi123i 1092
Description: Join 3 biconditionals with conjunction. (Contributed by NM, 21-Apr-1994.)
Hypotheses
Ref Expression
bi3.1
bi3.2
bi3.3
Assertion
Ref Expression
3anbi123i

Proof of Theorem 3anbi123i
StepHypRef Expression
1 bi3.1 . . . 4
2 bi3.2 . . . 4
31, 2anbi12i 433 . . 3
4 bi3.3 . . 3
53, 4anbi12i 433 . 2
6 df-3an 886 . 2
7 df-3an 886 . 2
85, 6, 73bitr4i 201 1
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   w3a 884
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 886
This theorem is referenced by:  3anbi1i  1094  3anbi2i  1095  3anbi3i  1096  syl3anb  1177  ne3anior  2287
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