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Theorem fvopab4ndm 5828
 Description: Value of a function given by an ordered-pair class abstraction, outside of its domain. (Contributed by NM, 28-Mar-2008.)
Hypothesis
Ref Expression
fvopab4ndm.1
Assertion
Ref Expression
fvopab4ndm
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem fvopab4ndm
StepHypRef Expression
1 fvopab4ndm.1 . . . . . 6
21dmeqi 5074 . . . . 5
3 dmopabss 5084 . . . . 5
42, 3eqsstri 3380 . . . 4
54sseli 3346 . . 3
65con3i 130 . 2
7 ndmfv 5758 . 2
86, 7syl 16 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   wceq 1653   wcel 1726  c0 3630  copab 4268   cdm 4881  cfv 5457 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406 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-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 4216  df-opab 4270  df-dm 4891  df-iota 5421  df-fv 5465
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