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Theorem csbfv12gALT 5739
 Description: Move class substitution in and out of a function value.(This is csbfv12g 5738 with a shortened proof, shortened by Alan Sare, 10-Nov-2012.) The proof is derived from the virtual deduction proof csbfv12gALTVD 29011. Although the proof is shorter, the total number of steps of all theorems used in the proof is probably longer. (Contributed by NM, 10-Nov-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
csbfv12gALT

Proof of Theorem csbfv12gALT
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbunig 4023 . . 3
2 csbabg 3310 . . . . 5
3 sbceqg 3267 . . . . . . 7
4 csbima12g 5213 . . . . . . . . 9
5 csbsng 3867 . . . . . . . . . 10
65imaeq2d 5203 . . . . . . . . 9
74, 6eqtrd 2468 . . . . . . . 8
8 csbconstg 3265 . . . . . . . 8
97, 8eqeq12d 2450 . . . . . . 7
103, 9bitrd 245 . . . . . 6
1110abbidv 2550 . . . . 5
122, 11eqtrd 2468 . . . 4
1312unieqd 4026 . . 3
141, 13eqtrd 2468 . 2
15 dffv4 5725 . . 3
1615csbeq2i 3277 . 2
17 dffv4 5725 . 2
1814, 16, 173eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2422  wsbc 3161  csb 3251  csn 3814  cuni 4015  cima 4881  cfv 5454 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-13 1727  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-pow 4377  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-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  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-uni 4016  df-br 4213  df-opab 4267  df-xp 4884  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fv 5462
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