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Mirrors > Home > ILE Home > Th. List > sb8e | Unicode version |
Description: Substitution of variable in existential quantifier. (Contributed by NM, 12-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Jim Kingdon, 15-Jan-2018.) |
Ref | Expression |
---|---|
sb8e.1 |
Ref | Expression |
---|---|
sb8e |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb8e.1 | . 2 | |
2 | 1 | nfs1 1765 | . 2 |
3 | sbequ12 1729 | . 2 | |
4 | 1, 2, 3 | cbvex 1714 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wnf 1421 wex 1453 wsb 1720 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 |
This theorem is referenced by: sb8mo 1991 mo2n 2005 mor 2019 nfrexdya 2447 |
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