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Theorem csbcom 3796
 Description: Commutative law for double substitution into a class. (Contributed by NM, 14-Nov-2005.) (Revised by NM, 18-Aug-2018.)
Assertion
Ref Expression
csbcom
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem csbcom
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbccom 3372 . . . 4
2 sbcel2 3790 . . . . 5
32sbcbii 3352 . . . 4
4 sbcel2 3790 . . . . 5
54sbcbii 3352 . . . 4
61, 3, 53bitr3i 275 . . 3
7 sbcel2 3790 . . 3
8 sbcel2 3790 . . 3
96, 7, 83bitr3i 275 . 2
109eqriv 2450 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1370   wcel 1758  wsbc 3292  csb 3394 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-fal 1376  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3078  df-sbc 3293  df-csb 3395  df-dif 3438  df-in 3442  df-ss 3449  df-nul 3745 This theorem is referenced by:  ovmpt2s  6323  fvmpt2curryd  6899
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