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Mirrors > Home > MPE Home > Th. List > nfaba1g | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 2374. See nfaba1 2917 for a version with a disjoint variable condition, but not requiring ax-13 2374. (Contributed by Mario Carneiro, 14-Oct-2016.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfaba1g | ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2152 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfabg 2916 | 1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1540 {cab 2717 Ⅎwnfc 2889 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2015 ax-10 2141 ax-11 2158 ax-12 2175 ax-13 2374 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-tru 1545 df-ex 1787 df-nf 1791 df-sb 2072 df-clab 2718 df-nfc 2891 |
This theorem is referenced by: (None) |
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