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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.) |
Ref | Expression |
---|---|
nfaba1 | ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2028 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfab 2769 | 1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1481 {cab 2608 Ⅎwnfc 2751 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-nfc 2753 |
This theorem is referenced by: nfopd 4419 nfimad 5475 nfiota1 5853 nffvd 6200 nfunidALT2 34256 nfunidALT 34257 nfopdALT 34258 setrec1 42438 |
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