Theorem mpt2mpt 6394

Description: Express a two-argument function as a one-argument function, or vice-versa. (Contributed by Mario Carneiro, 17-Dec-2013.) (Revised by Mario Carneiro, 29-Dec-2014.)

Hypothesis

Ref	Expression
mpt2mpt.1

Assertion

Ref	Expression
mpt2mpt

Distinct variable groups:   ,,,   ,,   ,,   ,   ,

Proof of Theorem mpt2mpt

Step	Hyp	Ref	Expression
1		iunxpconst 5061	. . 3
2		mpteq1 4532	. . 3
3	1, 2	ax-mp 5	. 2
4		mpt2mpt.1	. . 3
5	4	mpt2mptx 6393	. 2
6	3, 5	eqtr3i 2488	1

Syntax hints:  ->wi 4  =wceq 1395  {csn 4029  <.cop 4035  U_ciun 4330  e.cmpt 4510  X.cxp 5002  e.cmpt2 6298

This theorem is referenced by:  fconstmpt2  6397  fnov  6410  fmpt2co  6883  xpf1o  7699  resfval2  15262  catcisolem  15433  xpccatid  15457  curf2ndf  15516  evlslem4OLD  18173  evlslem4  18174  mdetunilem9  19122  txbas  20068  cnmpt1st  20169  cnmpt2nd  20170  cnmpt2c  20171  cnmpt2t  20174  txhmeo  20304  txswaphmeolem  20305  ptuncnv  20308  ptunhmeo  20309  xpstopnlem1  20310  xkohmeo  20316  prdstmdd  20622  ucnimalem  20783  fmucndlem  20794  fsum2cn  21375  fimaproj  27836  idfusubc0  32591  lmod1zr  33094

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