Theorem sn-base0 42468

Description: Avoid axioms in base0 17143 by using the discouraged df-base 17139. 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 17139	. 2 ⊢ Base = Slot 1
2	1	str0 17118	1 ⊢ ∅ = (Base‘∅)

Syntax hints:   = wceq 1540  ∅c0 4286  ‘cfv 6486  1c1 11029  Basecbs 17138

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 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701  ax-sep 5238  ax-nul 5248  ax-pr 5374

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 2066  df-mo 2533  df-eu 2562  df-clab 2708  df-cleq 2721  df-clel 2803  df-nfc 2878  df-ne 2926  df-ral 3045  df-rex 3054  df-rab 3397  df-v 3440  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4479  df-sn 4580  df-pr 4582  df-op 4586  df-uni 4862  df-br 5096  df-opab 5158  df-mpt 5177  df-id 5518  df-xp 5629  df-rel 5630  df-cnv 5631  df-co 5632  df-dm 5633  df-iota 6442  df-fun 6488  df-fv 6494  df-slot 17111  df-base 17139

This theorem is referenced by: (None)