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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfttrcl | Structured version Visualization version GIF version |
Description: Bound variable hypothesis builder for transitive closure. (Contributed by Scott Fenton, 17-Oct-2024.) |
Ref | Expression |
---|---|
nfttrcl.1 | ⊢ Ⅎ𝑥𝑅 |
Ref | Expression |
---|---|
nfttrcl | ⊢ Ⅎ𝑥t++𝑅 |
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 |
Colors of variables: wff setvar class |
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) |
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