Theorem nfttrcl 9627

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 9626	. 2 ⊢ (⊤ → Ⅎ𝑥t++𝑅)
4	3	mptru 1555	1 ⊢ Ⅎ𝑥t++𝑅

Syntax hints:  ⊤wtru 1549  Ⅎwnfc 2888  t++cttrcl 9623

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 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-10 2154  ax-11 2170  ax-12 2191  ax-ext 2713

This theorem depends on definitions:  df-bi 209  df-an 398  df-or 855  df-3an 1095  df-tru 1551  df-fal 1561  df-ex 1788  df-nf 1792  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-nfc 2890  df-ral 3056  df-rex 3066  df-rab 3394  df-v 3435  df-dif 3888  df-un 3890  df-ss 3902  df-nul 4265  df-if 4458  df-sn 4559  df-pr 4561  df-op 4565  df-br 5076  df-opab 5138  df-ttrcl 9624

This theorem is referenced by: (None)