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Mirrors > Home > MPE Home > Th. List > 2albidv | Structured version Visualization version GIF version |
Description: Formula-building rule for two universal quantifiers (deduction form). (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 2019 | . 2 ⊢ (𝜑 → (∀𝑦𝜓 ↔ ∀𝑦𝜒)) |
3 | 2 | albidv 2019 | 1 ⊢ (𝜑 → (∀𝑥∀𝑦𝜓 ↔ ∀𝑥∀𝑦𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 198 ∀wal 1654 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 |
This theorem depends on definitions: df-bi 199 |
This theorem is referenced by: dff13 6767 qliftfun 8097 seqf1o 13136 fi1uzind 13568 brfi1indALT 13571 trclfvcotr 14127 dchrelbas3 25376 isch2 28624 mclsssvlem 31994 mclsval 31995 mclsax 32001 mclsind 32002 trer 32838 mbfresfi 33992 isass 34180 relcnveq2 34635 elrelscnveq2 34784 elsymrels3 34841 elsymrels5 34843 eltrrels3 34867 eleqvrels3 34878 lpolsetN 37550 islpolN 37551 ismrc 38101 2sbc6g 39448 |
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