Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ovmpt2 Unicode version

Theorem ovmpt2 5636
 Description: Value of an operation given by a maps-to rule. Special case. (Contributed by NM, 16-May-1995.) (Revised by David Abernethy, 19-Jun-2012.)
Hypotheses
Ref Expression
ovmpt2g.1
ovmpt2g.2
ovmpt2g.3
ovmpt2.4
Assertion
Ref Expression
ovmpt2
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem ovmpt2
StepHypRef Expression
1 ovmpt2.4 . 2
2 ovmpt2g.1 . . 3
3 ovmpt2g.2 . . 3
4 ovmpt2g.3 . . 3
52, 3, 4ovmpt2g 5635 . 2
61, 5mp3an3 1221 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243   wcel 1393  cvv 2557  (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:  ixxval  8765  fzval  8876
 Copyright terms: Public domain W3C validator