Theorem nfttrcl 9736

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 9735	. 2 ⊢ (⊤ → Ⅎ𝑥t++𝑅)
4	3	mptru 1577	1 ⊢ Ⅎ𝑥t++𝑅

This proof depends on syntax axioms:  ⊤wtru 1571  Ⅎwnfc 2911  t++cttrcl 9732

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-10 2180  ax-11 2197  ax-12 2216  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-nf 1817  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-nfc 2913  df-ral 3081  df-rex 3091  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-br 5107  df-opab 5171  df-ttrcl 9733

This theorem is used by: (None)