Theorem cnvimarndmOLD 6099

Description: Obsolete version of cnvimarndm 6098 as of 29-Sep-2026. (Contributed by Jeff Hankins, 15-Jul-2009.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
cnvimarndmOLD	⊢ (◡𝐴 “ ran 𝐴) = dom 𝐴

Proof of Theorem cnvimarndmOLD

Step	Hyp	Ref	Expression
1		imadmrn 6085	. 2 ⊢ (◡𝐴 “ dom ◡𝐴) = ran ◡𝐴
2		df-rn 5669	. . 3 ⊢ ran 𝐴 = dom ◡𝐴
3	2	imaeq2i 6068	. 2 ⊢ (◡𝐴 “ ran 𝐴) = (◡𝐴 “ dom ◡𝐴)
4		dfdm4 5889	. 2 ⊢ dom 𝐴 = ran ◡𝐴
5	1, 3, 4	3eqtr4i 2796	1 ⊢ (◡𝐴 “ ran 𝐴) = dom 𝐴

This proof depends on syntax axioms:   = wceq 1570  ^◡ccnv 5657  dom cdm 5658  ran crn 5659   “ cima 5661

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5255  ax-pr 5398

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-ral 3081  df-rex 3091  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4841  df-br 5109  df-opab 5174  df-xp 5664  df-cnv 5666  df-dm 5668  df-rn 5669  df-res 5670  df-ima 5671

This theorem is used by: (None)