Theorem nfttrcl 9668

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 9667	. 2 ⊢ (⊤ → Ⅎ𝑥t++𝑅)
4	3	mptru 1569	1 ⊢ Ⅎ𝑥t++𝑅

Syntax hints:  ⊤wtru 1563  Ⅎwnfc 2911  t++cttrcl 9664

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-10 2177  ax-11 2193  ax-12 2214  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1101  df-tru 1565  df-fal 1575  df-ex 1802  df-nf 1806  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-nfc 2913  df-ral 3079  df-rex 3089  df-rab 3417  df-v 3458  df-dif 3909  df-un 3911  df-ss 3923  df-nul 4288  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-br 5103  df-opab 5165  df-ttrcl 9665

This theorem is referenced by: (None)