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Mirrors > Home > ILE Home > Th. List > 2albii | GIF version |
Description: Inference adding 2 universal quantifiers to both sides of an equivalence. (Contributed by NM, 9-Mar-1997.) |
Ref | Expression |
---|---|
albii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
2albii | ⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑥∀𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | albii.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
2 | 1 | albii 1405 | . 2 ⊢ (∀𝑦𝜑 ↔ ∀𝑦𝜓) |
3 | 2 | albii 1405 | 1 ⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑥∀𝑦𝜓) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∀wal 1288 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: mor 1991 mo4f 2009 moanim 2023 2eu4 2042 ralcomf 2529 raliunxp 4590 cnvsym 4828 intasym 4829 intirr 4831 codir 4833 qfto 4834 dffun4 5039 dffun4f 5044 funcnveq 5090 fun11 5094 fununi 5095 mpt22eqb 5768 addnq0mo 7060 mulnq0mo 7061 addsrmo 7343 mulsrmo 7344 |
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