Theorem cnvimarndmOLD 6082

Description: Obsolete version of cnvimarndm 6081 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 6068	. 2 ⊢ (◡𝐴 “ dom ◡𝐴) = ran ◡𝐴
2		df-rn 5661	. . 3 ⊢ ran 𝐴 = dom ◡𝐴
3	2	imaeq2i 6051	. 2 ⊢ (◡𝐴 “ ran 𝐴) = (◡𝐴 “ dom ◡𝐴)
4		dfdm4 5877	. 2 ⊢ dom 𝐴 = ran ◡𝐴
5	1, 3, 4	3eqtr4i 2793	1 ⊢ (◡𝐴 “ ran 𝐴) = dom 𝐴

This proof depends on syntax axioms:   = wceq 1569  ^◡ccnv 5649  dom cdm 5650  ran crn 5651   “ cima 5653

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-sep 5248  ax-pr 5390

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-ral 3077  df-rex 3087  df-rab 3413  df-v 3452  df-ss 3897  df-dif 4046  df-in 4090  df-un 4150  df-nul 4278  df-if 4482  df-sn 4585  df-pr 4587  df-op 4835  df-br 5103  df-opab 5167  df-xp 5656  df-cnv 5658  df-dm 5660  df-rn 5661  df-res 5662  df-ima 5663

This theorem is used by: (None)