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Mirrors > Home > ILE Home > Th. List > nfre1 | GIF version |
Description: 𝑥 is not free in ∃𝑥 ∈ 𝐴𝜑. (Contributed by NM, 19-Mar-1997.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfre1 | ⊢ Ⅎ𝑥∃𝑥 ∈ 𝐴 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 | . 2 ⊢ (∃𝑥 ∈ 𝐴 𝜑 ↔ ∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfe1 1385 | . 2 ⊢ Ⅎ𝑥∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1363 | 1 ⊢ Ⅎ𝑥∃𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff set class |
Syntax hints: ∧ wa 97 Ⅎwnf 1349 ∃wex 1381 ∈ wcel 1393 ∃wrex 2307 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-rex 2312 |
This theorem is referenced by: nfiu1 3687 fun11iun 5147 eusvobj2 5498 prarloclem3step 6594 prmuloc2 6665 ltexprlemm 6698 caucvgprprlemaddq 6806 caucvgsrlemgt1 6879 lbzbi 8551 |
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