Theorem sn-base0 42479

Description: Avoid axioms in base0 17284 by using the discouraged df-base 17280. 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 17280	. 2 ⊢ Base = Slot 1
2	1	str0 17257	1 ⊢ ∅ = (Base‘∅)

Syntax hints:   = wceq 1537  ∅c0 4353  ‘cfv 6577  1c1 11189  Basecbs 17279

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2158  ax-12 2178  ax-ext 2711  ax-sep 5319  ax-nul 5326  ax-pr 5449

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-nf 1782  df-sb 2065  df-mo 2543  df-eu 2572  df-clab 2718  df-cleq 2732  df-clel 2819  df-nfc 2895  df-ne 2947  df-ral 3068  df-rex 3077  df-rab 3445  df-v 3491  df-dif 3980  df-un 3982  df-ss 3994  df-nul 4354  df-if 4550  df-sn 4650  df-pr 4652  df-op 4656  df-uni 4934  df-br 5169  df-opab 5231  df-mpt 5252  df-id 5595  df-xp 5708  df-rel 5709  df-cnv 5710  df-co 5711  df-dm 5712  df-iota 6529  df-fun 6579  df-fv 6585  df-slot 17250  df-base 17280

This theorem is referenced by: (None)