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Mirrors > Home > MPE Home > Th. List > nfra2wOLD | Structured version Visualization version GIF version |
Description: Obsolete version of nfra2w 3139 as of 24-Sep-2024. (Contributed by Alan Sare, 31-Dec-2011.) (Revised by Gino Giotto, 10-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfra2wOLD | ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2897 | . 2 ⊢ Ⅎ𝑦𝐴 | |
2 | nfra1 3130 | . 2 ⊢ Ⅎ𝑦∀𝑦 ∈ 𝐵 𝜑 | |
3 | 1, 2 | nfralw 3137 | 1 ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1791 ∀wral 3051 |
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 2018 ax-8 2114 ax-10 2143 ax-11 2160 ax-12 2177 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-ex 1788 df-nf 1792 df-clel 2809 df-nfc 2879 df-ral 3056 |
This theorem is referenced by: (None) |
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