Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2448 | . 2 ⊢ (∃𝑥 ∈ 𝐴 𝜑 ↔ ∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfe1 1483 | . 2 ⊢ Ⅎ𝑥∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1461 | 1 ⊢ Ⅎ𝑥∃𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 Ⅎwnf 1447 ∃wex 1479 ∈ wcel 2135 ∃wrex 2443 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie1 1480 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-rex 2448 |
This theorem is referenced by: r19.29an 2606 nfiu1 3890 fun11iun 5447 eusvobj2 5822 fodjuomnilemdc 7099 ismkvnex 7110 prarloclem3step 7428 prmuloc2 7499 ltexprlemm 7532 caucvgprprlemaddq 7640 caucvgsrlemgt1 7727 axpre-suploclemres 7833 supinfneg 9524 infsupneg 9525 lbzbi 9545 divalglemeunn 11843 divalglemeuneg 11845 bezoutlemmain 11916 bezout 11929 pw1nct 13717 isomninnlem 13743 trirec0 13757 ismkvnnlem 13765 |
Copyright terms: Public domain | W3C validator |