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Theorem csbfv12g 5497
 Description: Move class substitution in and out of a function value. (Contributed by NM, 11-Nov-2005.)
Assertion
Ref Expression
csbfv12g

Proof of Theorem csbfv12g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbiotag 5156 . . 3
2 sbcbrg 4014 . . . . 5
3 csbconstg 3041 . . . . . 6
43breq2d 3973 . . . . 5
52, 4bitrd 187 . . . 4
65iotabidv 5149 . . 3
71, 6eqtrd 2187 . 2
8 df-fv 5171 . . 3
98csbeq2i 3054 . 2
10 df-fv 5171 . 2
117, 9, 103eqtr4g 2212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332   wcel 2125  wsbc 2933  csb 3027   class class class wbr 3961  cio 5126  cfv 5163 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-rex 2438  df-v 2711  df-sbc 2934  df-csb 3028  df-un 3102  df-sn 3562  df-pr 3563  df-op 3565  df-uni 3769  df-br 3962  df-iota 5128  df-fv 5171 This theorem is referenced by:  csbfv2g  5498
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