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Mirrors > Home > ILE Home > Th. List > 2albidv | GIF version |
Description: Formula-building rule for 2 existential quantifiers (deduction rule). (Contributed by NM, 4-Mar-1997.) |
Ref | Expression |
---|---|
2albidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
2albidv | ⊢ (𝜑 → (∀𝑥∀𝑦𝜓 ↔ ∀𝑥∀𝑦𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2albidv.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | 1 | albidv 1705 | . 2 ⊢ (𝜑 → (∀𝑦𝜓 ↔ ∀𝑦𝜒)) |
3 | 2 | albidv 1705 | 1 ⊢ (𝜑 → (∀𝑥∀𝑦𝜓 ↔ ∀𝑥∀𝑦𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 98 ∀wal 1241 |
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-17 1419 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: dff13 5407 qliftfun 6188 |
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