Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nd5 | GIF version |
Description: A lemma for proving conditionless ZFC axioms. (Contributed by NM, 8-Jan-2002.) |
Ref | Expression |
---|---|
nd5 | ⊢ (¬ ∀𝑦 𝑦 = 𝑥 → (𝑧 = 𝑦 → ∀𝑥 𝑧 = 𝑦)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dveeq2 1803 | . 2 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → (𝑧 = 𝑦 → ∀𝑥 𝑧 = 𝑦)) | |
2 | 1 | nalequcoms 1505 | 1 ⊢ (¬ ∀𝑦 𝑦 = 𝑥 → (𝑧 = 𝑦 → ∀𝑥 𝑧 = 𝑦)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1341 = wceq 1343 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 |
This theorem depends on definitions: df-bi 116 df-nf 1449 df-sb 1751 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |