Theorem csbiedf 3455

Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 13-Oct-2016.)

Hypotheses

Ref	Expression
csbiedf.1
csbiedf.2
csbiedf.3
csbiedf.4

Assertion

Ref	Expression
csbiedf

Distinct variable group:   ,

Proof of Theorem csbiedf

Step	Hyp	Ref	Expression
1		csbiedf.1	. . 3
2		csbiedf.4	. . . 4
3	2	ex 434	. . 3
4	1, 3	alrimi 1877	. 2
5		csbiedf.3	. . 3
6		csbiedf.2	. . 3
7		csbiebt 3454	. . 3
8	5, 6, 7	syl2anc 661	. 2
9	4, 8	mpbid 210	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  [_csb 3434

This theorem is referenced by:  csbied  3461  csbie2t  3463  natpropd  15345  fucpropd  15346  gsummptf1o  16990  sumsnd  31401  fsumsplit1  31573  fprodsplit1f  31593

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435