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Theorem csbnestgf 3300
 Description: Nest the composition of two substitutions. (Contributed by NM, 23-Nov-2005.) (Proof shortened by Mario Carneiro, 10-Nov-2016.)
Assertion
Ref Expression
csbnestgf

Proof of Theorem csbnestgf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2965 . . 3
2 df-csb 3253 . . . . . . 7
32abeq2i 2544 . . . . . 6
43sbcbii 3217 . . . . 5
5 nfcr 2565 . . . . . . 7
65alimi 1569 . . . . . 6
7 sbcnestgf 3299 . . . . . 6
86, 7sylan2 462 . . . . 5
94, 8syl5bb 250 . . . 4
109abbidv 2551 . . 3
111, 10sylan 459 . 2
12 df-csb 3253 . 2
13 df-csb 3253 . 2
1411, 12, 133eqtr4g 2494 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wnf 1554   wceq 1653   wcel 1726  cab 2423  wnfc 2560  cvv 2957  wsbc 3162  csb 3252 This theorem is referenced by:  csbnestg  3302  csbnest1g  3304 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-sbc 3163  df-csb 3253
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