Theorem ontrciOLD 6446

Description: Obsolete version of ontr 6443 as of 28-Dec-2024. (Contributed by NM, 11-Jun-1994.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
on.1	⊢ 𝐴 ∈ On

Assertion

Ref	Expression
ontrciOLD	⊢ Tr 𝐴

Proof of Theorem ontrciOLD

Step	Hyp	Ref	Expression
1		on.1	. 2 ⊢ 𝐴 ∈ On
2		ontr 6443	. 2 ⊢ (𝐴 ∈ On → Tr 𝐴)
3	1, 2	ax-mp 5	1 ⊢ Tr 𝐴

Syntax hints:   ∈ wcel 2109  Tr wtr 5214  Oncon0 6332

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-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ral 3045  df-v 3449  df-ss 3931  df-uni 4872  df-tr 5215  df-po 5546  df-so 5547  df-fr 5591  df-we 5593  df-ord 6335  df-on 6336

This theorem is referenced by: (None)