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Definition df-bic 26143
Description: Function that returns two propositions joined with 
<->. Experimental. (Contributed by FL, 2-Feb-2014.)
Assertion
Ref Expression
df-bic  |-  bi c  =  ( x  e.  ( ( Kleene `  NN )  ^m  { 1 ,  2 } )  |->  ( (  <=> c  conc  ( x `
 1 ) ) 
conc  ( x ` 
2 ) ) )

Detailed syntax breakdown of Definition df-bic
StepHypRef Expression
1 cbic 26142 . 2  class  bi c
2 vx . . 3  set  x
3 cn 9762 . . . . 5  class  NN
4 ckln 26083 . . . . 5  class  Kleene
53, 4cfv 5271 . . . 4  class  ( Kleene `  NN )
6 c1 8754 . . . . 5  class  1
7 c2 9811 . . . . 5  class  2
86, 7cpr 3654 . . . 4  class  { 1 ,  2 }
9 cmap 6788 . . . 4  class  ^m
105, 8, 9co 5874 . . 3  class  ( (
Kleene `  NN )  ^m  { 1 ,  2 } )
11 cbis 26122 . . . . 5  class  <=> c
122cv 1631 . . . . . 6  class  x
136, 12cfv 5271 . . . . 5  class  ( x `
 1 )
14 cconc 26107 . . . . 5  class  conc
1511, 13, 14co 5874 . . . 4  class  (  <=> c  conc  ( x `
 1 ) )
167, 12cfv 5271 . . . 4  class  ( x `
 2 )
1715, 16, 14co 5874 . . 3  class  ( (  <=>
c  conc  ( x `  1 ) ) 
conc  ( x ` 
2 ) )
182, 10, 17cmpt 4093 . 2  class  ( x  e.  ( ( Kleene `  NN )  ^m  {
1 ,  2 } )  |->  ( (  <=> c  conc  ( x `
 1 ) ) 
conc  ( x ` 
2 ) ) )
191, 18wceq 1632 1  wff  bi c  =  ( x  e.  ( ( Kleene `  NN )  ^m  { 1 ,  2 } )  |->  ( (  <=> c  conc  ( x `
 1 ) ) 
conc  ( x ` 
2 ) ) )
Colors of variables: wff set class
This definition is referenced by:  fnckle  26148  pfsubkl  26150
  Copyright terms: Public domain W3C validator