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Mirrors > Home > MPE Home > Th. List > nfaba1 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.) Add disjoint variable condition to avoid ax-13 2386. See nfaba1g 2987 for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 20-Jan-2024.) |
Ref | Expression |
---|---|
nfaba1 | ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2151 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfab 2984 | 1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1531 {cab 2799 Ⅎwnfc 2961 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-10 2141 ax-11 2157 ax-12 2173 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-nfc 2963 |
This theorem is referenced by: nfopd 4813 nfimad 5932 nfiota1 6310 nffvd 6676 nfunidALT2 36099 nfunidALT 36100 nfopdALT 36101 setrec1 44788 |
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