Theorem dmmpt2g 6873

Description: Domain of an operation given by the "maps to" notation, closed form of dmmpt2 6870. Caution: This theorem is only valid in the very special case where the value of the mapping is a constant! (Contributed by Alexander van der Vekens, 1-Jun-2017.) (Prove shortened by AV, 10-Feb-2019.)

Hypothesis

Ref	Expression
dmmpt2g.f

Assertion

Ref	Expression
dmmpt2g

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

Proof of Theorem dmmpt2g

Step	Hyp	Ref	Expression
1		simpl 457	. . 3
2	1	ralrimivva 2878	. 2
3		dmmpt2g.f	. . 3
4	3	dmmpt2ga 6872	. 2
5	2, 4	syl 16	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  X.cxp 5002  domcdm 5004  e.cmpt2 6298

This theorem is referenced by:  aovmpt4g  32286

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-8 1820  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-pow 4630  ax-pr 4691  ax-un 6592

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-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-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-fv 5601  df-oprab 6300  df-mpt2 6301  df-1st 6800  df-2nd 6801