Theorem ineq12i 3697

Description: Equality inference for intersection of two classes. (Contributed by NM, 24-Jun-2004.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)

Hypotheses

Ref	Expression
ineq1i.1
ineq12i.2

Assertion

Ref	Expression
ineq12i

Proof of Theorem ineq12i

Step	Hyp	Ref	Expression
1		ineq1i.1	. 2
2		ineq12i.2	. 2
3		ineq12 3694	. 2
4	1, 2, 3	mp2an 672	1

Syntax hints:  =wceq 1395  i^icin 3474

This theorem is referenced by:  undir  3746  difundi  3749  difindir  3752  inrab  3769  inrab2  3770  dfif4  3956  dfif5  3957  inxp  5140  resindi  5294  resindir  5295  rnin  5420  inimass  5427  funtp  5645  orduniss2  6668  offres  6795  fodomr  7688  wemapwe  8160  wemapweOLD  8161  explecnv  13676  psssdm2  15845  ablfacrp  17117  pjfval2  18740  ofco2  18953  iundisj2  21959  lejdiri  26457  cmbr3i  26518  nonbooli  26569  5oai  26579  3oalem5  26584  mayetes3i  26648  mdexchi  27254  disjpreima  27445  disjxpin  27447  iundisj2f  27449  xppreima  27487  iundisj2fi  27602  xpinpreima  27888  xpinpreima2  27889  ordtcnvNEW  27902  predin  29269  pprodcnveq  29533  dfiota3  29573  ptrest  30048  ftc1anclem6  30095  dnwech  30994  fgraphopab  31170  onfrALTlem5  33314  onfrALTlem4  33315  onfrALTlem5VD  33685  onfrALTlem4VD  33686  bj-inrab  34495  cotr3  37788

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-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-in 3482