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Theorem dffun6f 5468
 Description: Definition of function, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
dffun6f.1
dffun6f.2
Assertion
Ref Expression
dffun6f
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem dffun6f
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dffun3 5465 . 2
2 nfcv 2572 . . . . . . 7
3 dffun6f.2 . . . . . . 7
4 nfcv 2572 . . . . . . 7
52, 3, 4nfbr 4256 . . . . . 6
6 nfv 1629 . . . . . 6
7 breq2 4216 . . . . . 6
85, 6, 7cbvmo 2318 . . . . 5
98albii 1575 . . . 4
10 nfv 1629 . . . . . 6
1110mo2 2310 . . . . 5
1211albii 1575 . . . 4
13 nfcv 2572 . . . . . . 7
14 dffun6f.1 . . . . . . 7
15 nfcv 2572 . . . . . . 7
1613, 14, 15nfbr 4256 . . . . . 6
1716nfmo 2298 . . . . 5
18 nfv 1629 . . . . 5
19 breq1 4215 . . . . . 6
2019mobidv 2316 . . . . 5
2117, 18, 20cbval 1982 . . . 4
229, 12, 213bitr3ri 268 . . 3
2322anbi2i 676 . 2
241, 23bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  wmo 2282  wnfc 2559   class class class wbr 4212   wrel 4883   wfun 5448 This theorem is referenced by:  dffun6  5469  funopab  5486  funcnvmptOLD  24082  funcnvmpt  24083 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-id 4498  df-cnv 4886  df-co 4887  df-fun 5456
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