Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dffun6f Unicode version

Theorem dffun6f 5285
 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 5282 . 2
2 nfcv 2432 . . . . . . 7
3 dffun6f.2 . . . . . . 7
4 nfcv 2432 . . . . . . 7
52, 3, 4nfbr 4083 . . . . . 6
6 nfv 1609 . . . . . 6
7 breq2 4043 . . . . . 6
85, 6, 7cbvmo 2193 . . . . 5
98albii 1556 . . . 4
10 nfv 1609 . . . . . 6
1110mo2 2185 . . . . 5
1211albii 1556 . . . 4
13 nfcv 2432 . . . . . . 7
14 dffun6f.1 . . . . . . 7
15 nfcv 2432 . . . . . . 7
1613, 14, 15nfbr 4083 . . . . . 6
1716nfmo 2173 . . . . 5
18 nfv 1609 . . . . 5
19 breq1 4042 . . . . . 6
2019mobidv 2191 . . . . 5
2117, 18, 20cbval 1937 . . . 4
229, 12, 213bitr3ri 267 . . 3
2322anbi2i 675 . 2
241, 23bitr4i 243 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530  wex 1531   wceq 1632  wmo 2157  wnfc 2419   class class class wbr 4039   wrel 4710   wfun 5265 This theorem is referenced by:  dffun6  5286  funopab  5303  funcnvmptOLD  23249  funcnvmpt  23250 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-id 4325  df-cnv 4713  df-co 4714  df-fun 5273
 Copyright terms: Public domain W3C validator