Theorem ontrciOLD 6498

Description: Obsolete version of ontr 6495 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 6495	. 2 ⊢ (𝐴 ∈ On → Tr 𝐴)
3	1, 2	ax-mp 5	1 ⊢ Tr 𝐴

Syntax hints:   ∈ wcel 2106  Tr wtr 5265  Oncon0 6386

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-v 3480  df-ss 3980  df-uni 4913  df-tr 5266  df-po 5597  df-so 5598  df-fr 5641  df-we 5643  df-ord 6389  df-on 6390

This theorem is referenced by: (None)