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Theorem fgraphxp 27509
 Description: Express a function as a subset of the cross product. (Contributed by Stefan O'Rear, 25-Jan-2015.)
Assertion
Ref Expression
fgraphxp
Distinct variable groups:   ,   ,   ,

Proof of Theorem fgraphxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fgraphopab 27508 . 2
2 vex 2961 . . . . . . 7
3 vex 2961 . . . . . . 7
42, 3op1std 6359 . . . . . 6
54fveq2d 5734 . . . . 5
62, 3op2ndd 6360 . . . . 5
75, 6eqeq12d 2452 . . . 4
87rabxp 4916 . . 3
9 df-3an 939 . . . 4
109opabbii 4274 . . 3
118, 10eqtri 2458 . 2
121, 11syl6eqr 2488 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726  crab 2711  cop 3819  copab 4267   cxp 4878  wf 5452  cfv 5456  c1st 6349  c2nd 6350 This theorem is referenced by:  hausgraph  27510 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pow 4379  ax-pr 4405  ax-un 4703 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-fv 5464  df-1st 6351  df-2nd 6352
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