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Theorem f1ocnvfvrneq 5978
 Description: If the values of a one-to-one function for two arguments from the range of the function are equal, the arguments themselves must be equal. (Contributed by Alexander van der Vekens, 12-Nov-2017.)
Assertion
Ref Expression
f1ocnvfvrneq

Proof of Theorem f1ocnvfvrneq
StepHypRef Expression
1 f1f1orn 5644 . . 3
2 f1ocnv 5646 . . 3
3 f1of1 5632 . . . 4
4 f1veqaeq 5964 . . . . 5
54ex 424 . . . 4
63, 5syl 16 . . 3
71, 2, 63syl 19 . 2
87imp 419 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1649   wcel 1721  ccnv 4836   crn 4838  wf1 5410  wf1o 5412  cfv 5413 This theorem is referenced by:  nbgraf1olem5  21408  constr3trllem2  21591  usgra2adedgspthlem2  28044 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-sbc 3122  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-opab 4227  df-id 4458  df-xp 4843  df-rel 4844  df-cnv 4845  df-co 4846  df-dm 4847  df-rn 4848  df-iota 5377  df-fun 5415  df-fn 5416  df-f 5417  df-f1 5418  df-fo 5419  df-f1o 5420  df-fv 5421
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