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Theorem feq12d 5397
Description: Equality deduction for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypotheses
Ref Expression
feq12d.1  |-  ( ph  ->  F  =  G )
feq12d.2  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
feq12d  |-  ( ph  ->  ( F : A --> C 
<->  G : B --> C ) )

Proof of Theorem feq12d
StepHypRef Expression
1 feq12d.1 . . 3  |-  ( ph  ->  F  =  G )
21feq1d 5395 . 2  |-  ( ph  ->  ( F : A --> C 
<->  G : A --> C ) )
3 feq12d.2 . . 3  |-  ( ph  ->  A  =  B )
43feq2d 5396 . 2  |-  ( ph  ->  ( G : A --> C 
<->  G : B --> C ) )
52, 4bitrd 244 1  |-  ( ph  ->  ( F : A --> C 
<->  G : B --> C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1632   -->wf 5267
This theorem is referenced by:  feq123d  5398  smoeq  6383  oif  7261  catcisolem  13954  hofcl  14049  dmdprd  15252  dpjf  15308  pjf2  16630  lmbr2  17005  lmff  17045  dfac14  17328  lmmbr2  18701  lmcau  18754  perfdvf  19269  dvnfre  19317  dvle  19370  dvfsumle  19384  dvfsumge  19385  dvmptrecl  19387  ismeas  23545  isumgra  23882  eupap1  23915  fprg  25236  sdclem1  26556  dfac21  27267  iswlk  28329  istrl  28336  constr3trllem1  28396
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-fun 5273  df-fn 5274  df-f 5275
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