Theorem resmpt3 5329

Description: Unconditional restriction of the mapping operation. (Contributed by Stefan O'Rear, 24-Jan-2015.) (Proof shortened by Mario Carneiro, 22-Mar-2015.)

Assertion

Ref	Expression
resmpt3

Distinct variable groups:   ,   ,

Proof of Theorem resmpt3

Step	Hyp	Ref	Expression
1		resres 5291	. 2
2		ssid 3522	. . . 4
3		resmpt 5328	. . . 4
4	2, 3	ax-mp 5	. . 3
5	4	reseq1i 5274	. 2
6		inss1 3717	. . 3
7		resmpt 5328	. . 3
8	6, 7	ax-mp 5	. 2
9	1, 5, 8	3eqtr3i 2494	1

Syntax hints:  =wceq 1395  i^icin 3474  C_wss 3475  e.cmpt 4510  |`cres 5006

This theorem is referenced by:  offres  6795  lo1resb  13387  o1resb  13389  measinb2  28194  eulerpartgbij  28311

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-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  df-mpt 4512  df-xp 5010  df-rel 5011  df-res 5016