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Theorem cnvin 5418
Description: Distributive law for converse over intersection. Theorem 15 of [Suppes] p. 62. (Contributed by NM, 25-Mar-1998.) (Revised by Mario Carneiro, 26-Jun-2014.)
Assertion
Ref Expression
cnvin

Proof of Theorem cnvin
StepHypRef Expression
1 cnvdif 5417 . . 3
2 cnvdif 5417 . . . 4
32difeq2i 3618 . . 3
41, 3eqtri 2486 . 2
5 dfin4 3737 . . 3
65cnveqi 5182 . 2
7 dfin4 3737 . 2
84, 6, 73eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  \cdif 3472  i^icin 3474  `'ccnv 5003
This theorem is referenced by:  rnin  5420  dminxp  5452  imainrect  5453  cnvcnv  5464  pjdm  18738  ordtrest2  19705  ustexsym  20718  trust  20732  ordtcnvNEW  27902  ordtrest2NEW  27905  msrf  28902  elrn3  29192  pprodcnveq  29533
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-ral 2812  df-rex 2813  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-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012
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