Theorem opelopaba 4768

Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. (Contributed by Mario Carneiro, 19-Dec-2013.)

Hypotheses

Ref	Expression
opelopaba.1
opelopaba.2
opelopaba.3

Assertion

Ref	Expression
opelopaba

Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem opelopaba

Step	Hyp	Ref	Expression
1		opelopaba.1	. 2
2		opelopaba.2	. 2
3		opelopaba.3	. . 3
4	3	opelopabga 4765	. 2
5	1, 2, 4	mp2an 672	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  cvv 3109  <.cop 4035  {copab 4509

This theorem is referenced by:  canthwelem  9049  canthwe  9050  bcthlem1  21763  bj-elid  34599

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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511