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Theorem feqmptdf 23478
 Description: Deduction form of dffn5f 5684. (Contributed by Mario Carneiro, 8-Jan-2015.) (Revised by Thierry Arnoux, 10-May-2017.)
Hypotheses
Ref Expression
feqmptdf.1
feqmptdf.2
feqmptdf.3
Assertion
Ref Expression
feqmptdf

Proof of Theorem feqmptdf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 feqmptdf.3 . . 3
2 ffn 5495 . . 3
31, 2syl 15 . 2
4 fnrel 5447 . . . . . 6
5 feqmptdf.2 . . . . . . 7
6 nfcv 2502 . . . . . . 7
75, 6dfrel4 23441 . . . . . 6
84, 7sylib 188 . . . . 5
9 feqmptdf.1 . . . . . . 7
105, 9nffn 5445 . . . . . 6
11 nfv 1624 . . . . . 6
12 fnbr 5451 . . . . . . . . 9
1312ex 423 . . . . . . . 8
1413pm4.71rd 616 . . . . . . 7
15 eqcom 2368 . . . . . . . . 9
16 fnbrfvb 5670 . . . . . . . . 9
1715, 16syl5bb 248 . . . . . . . 8
1817pm5.32da 622 . . . . . . 7
1914, 18bitr4d 247 . . . . . 6
2010, 11, 19opabbid 4183 . . . . 5
218, 20eqtrd 2398 . . . 4
22 df-mpt 4181 . . . 4
2321, 22syl6eqr 2416 . . 3
24 fvex 5646 . . . . . 6
2524rgenw 2695 . . . . 5
269fnmptf 23477 . . . . 5
2725, 26ax-mp 8 . . . 4
28 fneq1 5438 . . . 4
2927, 28mpbiri 224 . . 3
3023, 29impbii 180 . 2
313, 30sylib 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1647   wcel 1715  wnfc 2489  wral 2628  cvv 2873   class class class wbr 4125  copab 4178   cmpt 4179   wrel 4797   wfn 5353  wf 5354  cfv 5358 This theorem is referenced by:  esumf1o  23910 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-14 1719  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347  ax-sep 4243  ax-nul 4251  ax-pr 4316 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 937  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-eu 2221  df-mo 2222  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-ne 2531  df-ral 2633  df-rex 2634  df-rab 2637  df-v 2875  df-sbc 3078  df-dif 3241  df-un 3243  df-in 3245  df-ss 3252  df-nul 3544  df-if 3655  df-sn 3735  df-pr 3736  df-op 3738  df-uni 3930  df-br 4126  df-opab 4180  df-mpt 4181  df-id 4412  df-xp 4798  df-rel 4799  df-cnv 4800  df-co 4801  df-dm 4802  df-iota 5322  df-fun 5360  df-fn 5361  df-f 5362  df-fv 5366
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