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Mirrors > Home > MPE Home > Th. List > nfcjust | Structured version Visualization version GIF version |
Description: Justification theorem for df-nfc 2938. (Contributed by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
nfcjust | ⊢ (∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 ↔ ∀𝑧Ⅎ𝑥 𝑧 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1w 2872 | . . 3 ⊢ (𝑦 = 𝑧 → (𝑦 ∈ 𝐴 ↔ 𝑧 ∈ 𝐴)) | |
2 | 1 | nfbidv 1923 | . 2 ⊢ (𝑦 = 𝑧 → (Ⅎ𝑥 𝑦 ∈ 𝐴 ↔ Ⅎ𝑥 𝑧 ∈ 𝐴)) |
3 | 2 | cbvalvw 2043 | 1 ⊢ (∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 ↔ ∀𝑧Ⅎ𝑥 𝑧 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ∀wal 1536 Ⅎwnf 1785 ∈ wcel 2111 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-nf 1786 df-clel 2870 |
This theorem is referenced by: (None) |
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