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Theorem mpt2eq3dva 5511
Description: Slightly more general equality inference for the maps to notation. (Contributed by NM, 17-Oct-2013.)
Hypothesis
Ref Expression
mpt2eq3dva.1  C  D
Assertion
Ref Expression
mpt2eq3dva  ,  |->  C  ,  |->  D
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)    C(,)    D(,)

Proof of Theorem mpt2eq3dva
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpt2eq3dva.1 . . . . . 6  C  D
213expb 1104 . . . . 5 
C  D
32eqeq2d 2048 . . . 4  C  D
43pm5.32da 425 . . 3  C  D
54oprabbidv 5501 . 2  { <. <. , 
>. ,  >.  |  C }  { <. <. , 
>. ,  >.  |  D }
6 df-mpt2 5460 . 2  ,  |->  C  { <. <. ,  >. ,  >.  |  C }
7 df-mpt2 5460 . 2  ,  |->  D  { <. <. ,  >. ,  >.  |  D }
85, 6, 73eqtr4g 2094 1  ,  |->  C  ,  |->  D
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   w3a 884   wceq 1242   wcel 1390   {coprab 5456    |-> cmpt2 5457
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-oprab 5459  df-mpt2 5460
This theorem is referenced by:  mpt2eq3ia  5512  ofeq  5656  fmpt2co  5779  iseqeq2  8895  iseqeq3  8896  iseqval  8900
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