Theorem nfttrcl 9664

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 9663	. 2 ⊢ (⊤ → Ⅎ𝑥t++𝑅)
4	3	mptru 1547	1 ⊢ Ⅎ𝑥t++𝑅

Syntax hints:  ⊤wtru 1541  Ⅎwnfc 2876  t++cttrcl 9660

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

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-clab 2708  df-cleq 2721  df-clel 2803  df-nfc 2878  df-ral 3045  df-rex 3054  df-rab 3406  df-v 3449  df-dif 3917  df-un 3919  df-ss 3931  df-nul 4297  df-if 4489  df-sn 4590  df-pr 4592  df-op 4596  df-br 5108  df-opab 5170  df-ttrcl 9661

This theorem is referenced by: (None)