Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ovmpt2x Unicode version

Theorem ovmpt2x 5657
 Description: The value of an operation class abstraction. Variant of ovmpt2ga 5658 which does not require and to be distinct. (Contributed by Jeff Madsen, 10-Jun-2010.) (Revised by Mario Carneiro, 20-Dec-2013.)
Hypotheses
Ref Expression
ovmpt2x.1
ovmpt2x.2
ovmpt2x.3
Assertion
Ref Expression
ovmpt2x
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem ovmpt2x
StepHypRef Expression
1 elex 2583 . 2
2 ovmpt2x.3 . . . 4
32a1i 9 . . 3
4 ovmpt2x.1 . . . 4
54adantl 266 . . 3
6 ovmpt2x.2 . . . 4
76adantl 266 . . 3
8 simp1 915 . . 3
9 simp2 916 . . 3
10 simp3 917 . . 3
113, 5, 7, 8, 9, 10ovmpt2dx 5655 . 2
121, 11syl3an3 1181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   w3a 896   wceq 1259   wcel 1409  cvv 2574  (class class class)co 5540   cmpt2 5542 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955  ax-pr 3972  ax-setind 4290 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-fal 1265  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ne 2221  df-ral 2328  df-rex 2329  df-v 2576  df-sbc 2788  df-dif 2948  df-un 2950  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-opab 3847  df-id 4058  df-xp 4379  df-rel 4380  df-cnv 4381  df-co 4382  df-dm 4383  df-iota 4895  df-fun 4932  df-fv 4938  df-ov 5543  df-oprab 5544  df-mpt2 5545 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator