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Mirrors > Home > NFE Home > Th. List > nfra1 | GIF version |
Description: x is not free in ∀x ∈ Aφ. (Contributed by NM, 18-Oct-1996.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfra1 | ⊢ Ⅎx∀x ∈ A φ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2619 | . 2 ⊢ (∀x ∈ A φ ↔ ∀x(x ∈ A → φ)) | |
2 | nfa1 1788 | . 2 ⊢ Ⅎx∀x(x ∈ A → φ) | |
3 | 1, 2 | nfxfr 1570 | 1 ⊢ Ⅎx∀x ∈ A φ |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 Ⅎwnf 1544 ∈ wcel 1710 ∀wral 2614 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 df-ral 2619 |
This theorem is referenced by: nfra2 2668 r19.12 2727 ralbi 2750 ralcom2 2775 nfss 3266 ralidm 3653 nfii1 3998 dfiun2g 3999 ncfinraise 4481 fun11iun 5305 chfnrn 5399 ffnfv 5427 mpteq12f 5655 mpt2eq123 5661 fvmptss 5705 |
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