Theorem ontrciOLD 6474

Description: Obsolete version of ontr 6471 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 6471	. 2 ⊢ (𝐴 ∈ On → Tr 𝐴)
3	1, 2	ax-mp 5	1 ⊢ Tr 𝐴

Syntax hints:   ∈ wcel 2107  Tr wtr 5265  Oncon0 6362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3063  df-v 3477  df-in 3955  df-ss 3965  df-uni 4909  df-tr 5266  df-po 5588  df-so 5589  df-fr 5631  df-we 5633  df-ord 6365  df-on 6366

This theorem is referenced by: (None)