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Theorem dfdmf 4528
 Description: Definition of domain, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
dfdmf.1
dfdmf.2
Assertion
Ref Expression
dfdmf
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem dfdmf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dm 4355 . 2
2 nfcv 2178 . . . . 5
3 dfdmf.2 . . . . 5
4 nfcv 2178 . . . . 5
52, 3, 4nfbr 3808 . . . 4
6 nfv 1421 . . . 4
7 breq2 3768 . . . 4
85, 6, 7cbvex 1639 . . 3
98abbii 2153 . 2
10 nfcv 2178 . . . . 5
11 dfdmf.1 . . . . 5
12 nfcv 2178 . . . . 5
1310, 11, 12nfbr 3808 . . . 4
1413nfex 1528 . . 3
15 nfv 1421 . . 3
16 breq1 3767 . . . 4
1716exbidv 1706 . . 3
1814, 15, 17cbvab 2160 . 2
191, 9, 183eqtri 2064 1
 Colors of variables: wff set class Syntax hints:   wceq 1243  wex 1381  cab 2026  wnfc 2165   class class class wbr 3764   cdm 4345 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-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-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-dm 4355 This theorem is referenced by:  dmopab  4546
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