Theorem sn-base0 42465

Description: Avoid axioms in base0 17231 by using the discouraged df-base 17227. This kind of axiom save is probably not worth it. (Contributed by SN, 16-Sep-2025.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
sn-base0	⊢ ∅ = (Base‘∅)

Proof of Theorem sn-base0

Step	Hyp	Ref	Expression
1		df-base 17227	. 2 ⊢ Base = Slot 1
2	1	str0 17206	1 ⊢ ∅ = (Base‘∅)

Syntax hints:   = wceq 1540  ∅c0 4308  ‘cfv 6530  1c1 11128  Basecbs 17226

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2707  ax-sep 5266  ax-nul 5276  ax-pr 5402

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2539  df-eu 2568  df-clab 2714  df-cleq 2727  df-clel 2809  df-nfc 2885  df-ne 2933  df-ral 3052  df-rex 3061  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-ss 3943  df-nul 4309  df-if 4501  df-sn 4602  df-pr 4604  df-op 4608  df-uni 4884  df-br 5120  df-opab 5182  df-mpt 5202  df-id 5548  df-xp 5660  df-rel 5661  df-cnv 5662  df-co 5663  df-dm 5664  df-iota 6483  df-fun 6532  df-fv 6538  df-slot 17199  df-base 17227

This theorem is referenced by: (None)