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Theorem csbiotag 4371
 Description: Class substitution within a description binder. (Contributed by Scott Fenton, 6-Oct-2017.)
Assertion
Ref Expression
csbiotag
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem csbiotag
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3139 . . 3
2 dfsbcq2 3049 . . . 4
32iotabidv 4360 . . 3
41, 3eqeq12d 2367 . 2
5 vex 2862 . . 3
6 nfs1v 2106 . . . 4
76nfiota 4343 . . 3
8 sbequ12 1919 . . . 4
98iotabidv 4360 . . 3
105, 7, 9csbief 3177 . 2
114, 10vtoclg 2914 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642  wsb 1648   wcel 1710  wsbc 3046  csb 3136  cio 4337 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047  df-csb 3137  df-sn 3741  df-uni 3892  df-iota 4339 This theorem is referenced by:  csbfv12g  5336
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