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Theorem conrel1d 37962
 Description: Deduction about composition with a class with no relational content. (Contributed by Richard Penner, 24-Dec-2019.)
Hypothesis
Ref Expression
conrel1d.a
Assertion
Ref Expression
conrel1d

Proof of Theorem conrel1d
StepHypRef Expression
1 incom 3687 . . 3
2 dfdm4 5205 . . . . 5
3 conrel1d.a . . . . . . 7
43rneqd 5240 . . . . . 6
5 rn0 5264 . . . . . 6
64, 5syl6eq 2514 . . . . 5
72, 6syl5eq 2510 . . . 4
8 ineq2 3690 . . . . 5
9 in0 3820 . . . . 5
108, 9syl6eq 2514 . . . 4
117, 10syl 16 . . 3
121, 11syl5eq 2510 . 2
1312coemptyd 12918 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1395   cin 3470  c0 3793  ccnv 5007   cdm 5008   crn 5009   ccom 5012 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  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 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-br 4457  df-opab 4516  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-dm 5018  df-rn 5019  df-res 5020 This theorem is referenced by: (None)
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