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Theorem fopab2g 25248
 Description: Functionality of an ordered-pair class abstraction given by the "maps to" notation. (Contributed by FL, 17-May-2010.) (Proof shortened by Mario Carneiro, 31-May-2014.)
Assertion
Ref Expression
fopab2g
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem fopab2g
StepHypRef Expression
1 feq1 5391 . 2
2 eqid 2296 . . 3
32fmpt 5697 . 2
41, 3syl6rbbr 255 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wceq 1632   wcel 1696  wral 2556   cmpt 4093  wf 5267 This theorem is referenced by:  domrancur1c  25305 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-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230 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-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-sbc 3005  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-uni 3844  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fun 5273  df-fn 5274  df-f 5275  df-fv 5279
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