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Theorem ovmpt2dx 5627
 Description: Value of an operation given by a maps-to rule, deduction form. (Contributed by Mario Carneiro, 29-Dec-2014.)
Hypotheses
Ref Expression
ovmpt2dx.1
ovmpt2dx.2
ovmpt2dx.3
ovmpt2dx.4
ovmpt2dx.5
ovmpt2dx.6
Assertion
Ref Expression
ovmpt2dx
Distinct variable groups:   ,,   ,   ,   ,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)   (,)

Proof of Theorem ovmpt2dx
StepHypRef Expression
1 ovmpt2dx.1 . 2
2 ovmpt2dx.2 . 2
3 ovmpt2dx.3 . 2
4 ovmpt2dx.4 . 2
5 ovmpt2dx.5 . 2
6 ovmpt2dx.6 . 2
7 nfv 1421 . 2
8 nfv 1421 . 2
9 nfcv 2178 . 2
10 nfcv 2178 . 2
11 nfcv 2178 . 2
12 nfcv 2178 . 2
131, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12ovmpt2dxf 5626 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  (class class class)co 5512   cmpt2 5514 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944  ax-setind 4262 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ne 2206  df-ral 2311  df-rex 2312  df-v 2559  df-sbc 2765  df-dif 2920  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-id 4030  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-iota 4867  df-fun 4904  df-fv 4910  df-ov 5515  df-oprab 5516  df-mpt2 5517 This theorem is referenced by:  ovmpt2d  5628  ovmpt2x  5629
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