Theorem nfttrcl 33507

Description: Bound variable hypothesis builder for transitive closure. (Contributed by Scott Fenton, 17-Oct-2024.)

Hypothesis

Ref	Expression
nfttrcl.1	⊢ Ⅎ𝑥𝑅

Assertion

Ref	Expression
nfttrcl	⊢ Ⅎ𝑥t++𝑅

Proof of Theorem nfttrcl

Step	Hyp	Ref	Expression
1		nfttrcl.1	. . . 4 ⊢ Ⅎ𝑥𝑅
2	1	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝑅)
3	2	nfttrcld 33506	. 2 ⊢ (⊤ → Ⅎ𝑥t++𝑅)
4	3	mptru 1550	1 ⊢ Ⅎ𝑥t++𝑅

Syntax hints:  ⊤wtru 1544  Ⅎwnfc 2884  t++cttrcl 33503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-nf 1792  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2886  df-ral 3063  df-rex 3064  df-rab 3067  df-v 3407  df-dif 3866  df-un 3868  df-nul 4235  df-if 4437  df-sn 4539  df-pr 4541  df-op 4545  df-br 5051  df-opab 5113  df-ttrcl 33504

This theorem is referenced by: (None)