Theorem ss2rabi 3581

Description: Inference of restricted abstraction subclass from implication. (Contributed by NM, 14-Oct-1999.)

Hypothesis

Ref	Expression
ss2rabi.1

Assertion

Ref	Expression
ss2rabi

Proof of Theorem ss2rabi

Step	Hyp	Ref	Expression
1		ss2rab 3575	. 2
2		ss2rabi.1	. 2
3	1, 2	mprgbir 2821	1

Syntax hints:  ->wi 4  e.wcel 1818  {crab 2811  C_wss 3475

This theorem is referenced by:  supub  7939  suplub  7940  card2on  8001  rankval4  8306  fin1a2lem12  8812  catlid  15080  catrid  15081  gsumval2  15907  lbsextlem3  17806  psrbagsn  18160  musum  23467  ppiub  23479  usisuslgra  24365  disjxwwlks  24736  clwlknclwlkdifnum  24961  bj-unrab  34494  lclkrs2  37267

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-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-nfc 2607  df-ral 2812  df-rab 2816  df-in 3482  df-ss 3489