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Theorem csbie2t 3180
Description: Conversion of implicit substitution to explicit substitution into a class (closed form of csbie2 3181). (Contributed by NM, 3-Sep-2007.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
csbie2t.1
csbie2t.2
Assertion
Ref Expression
csbie2t
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem csbie2t
StepHypRef Expression
1 nfa1 1788 . 2  F/
2 nfcvd 2490 . 2  F/_
3 csbie2t.1 . . 3
43a1i 10 . 2
5 nfa2 1855 . . . 4  F/
6 nfv 1619 . . . 4  F/
75, 6nfan 1824 . . 3  F/
8 nfcvd 2490 . . 3  F/_
9 csbie2t.2 . . . 4
109a1i 10 . . 3
11 sp 1747 . . . . 5
1211sps 1754 . . . 4
1312impl 603 . . 3
147, 8, 10, 13csbiedf 3173 . 2
151, 2, 4, 14csbiedf 3173 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358  wal 1540   wceq 1642   wcel 1710  cvv 2859  csb 3136
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-v 2861  df-sbc 3047  df-csb 3137
This theorem is referenced by:  csbie2  3181
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