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Mirrors > Home > MPE Home > Th. List > 19.21bbi | Structured version Visualization version GIF version |
Description: Inference removing two universal quantifiers. Version of 19.21bi 2186 with two quantifiers. (Contributed by NM, 20-Apr-1994.) |
Ref | Expression |
---|---|
19.21bbi.1 | ⊢ (𝜑 → ∀𝑥∀𝑦𝜓) |
Ref | Expression |
---|---|
19.21bbi | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.21bbi.1 | . . 3 ⊢ (𝜑 → ∀𝑥∀𝑦𝜓) | |
2 | 1 | 19.21bi 2186 | . 2 ⊢ (𝜑 → ∀𝑦𝜓) |
3 | 2 | 19.21bi 2186 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-12 2175 |
This theorem depends on definitions: df-bi 210 df-ex 1788 |
This theorem is referenced by: 2mo 2649 poclOLD 5473 funun 6423 fununi 6452 trclfvcotr 14569 acycgrcycl 32819 pm14.24 41721 |
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