Theorem sbcimg 3369

Description: Distribution of class substitution over implication. (Contributed by NM, 16-Jan-2004.)

Assertion

Ref	Expression
sbcimg

Proof of Theorem sbcimg

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfsbcq2 3330	. 2
2		dfsbcq2 3330	. . 3
3		dfsbcq2 3330	. . 3
4	2, 3	imbi12d 320	. 2
5		sbim 2136	. 2
6	1, 4, 5	vtoclbg 3168	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327

This theorem is referenced by:  sbcim1  3376  sbceqal  3383  sbcimdvOLD  3397  sbc19.21g  3400  sbcssg  3940  iota4an  5575  sbcfung  5616  riotass2  6284  tfinds2  6698  telgsums  17022  sbcimi  30512  sbcim2g  33309  sbcssOLD  33313  onfrALTlem5  33314  sbcim2gVD  33675  sbcssgVD  33683  onfrALTlem5VD  33685  bnj538OLD  33797  bnj110  33916  bnj92  33920  bnj539  33949  bnj540  33950  cdlemkid3N  36659  cdlemkid4  36660  cdlemk35s  36663  cdlemk39s  36665  cdlemk42  36667

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-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328