Theorem fconstmpt2 6397

Description: Representation of a constant operation using the mapping operation. (Contributed by SO, 11-Jul-2018.)

Assertion

Ref	Expression
fconstmpt2

Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem fconstmpt2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		fconstmpt 5048	. 2
2		eqidd 2458	. . 3
3	2	mpt2mpt 6394	. 2
4	1, 3	eqtri 2486	1

Syntax hints:  =wceq 1395  {csn 4029  <.cop 4035  e.cmpt 4510  X.cxp 5002  e.cmpt2 6298

This theorem is referenced by:  tposconst  7012  mat0op  18921  matsc  18952  mdetrsca2  19106  smadiadetglem2  19174

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-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-sbc 3328  df-csb 3435  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-iun 4332  df-opab 4511  df-mpt 4512  df-xp 5010  df-rel 5011  df-oprab 6300  df-mpt2 6301