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Mirrors > Home > MPE Home > Th. List > axc16nfOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of axc16nf 2122 as of 12-Oct-2021. (Contributed by Mario Carneiro, 7-Oct-2016.) Remove dependency on ax-11 2021. (Revised by Wolf Lammen, 9-Sep-2018.) (Proof shortened by BJ, 14-Jun-2019.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
axc16nfOLD | ⊢ (∀𝑥 𝑥 = 𝑦 → Ⅎ𝑧𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aev 1970 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧 𝑧 = 𝑤) | |
2 | nfa1 2015 | . . 3 ⊢ Ⅎ𝑧∀𝑧 𝑧 = 𝑤 | |
3 | axc16 2120 | . . 3 ⊢ (∀𝑧 𝑧 = 𝑤 → (𝜑 → ∀𝑧𝜑)) | |
4 | 2, 3 | nf5d 2104 | . 2 ⊢ (∀𝑧 𝑧 = 𝑤 → Ⅎ𝑧𝜑) |
5 | 1, 4 | syl 17 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → Ⅎ𝑧𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 Ⅎwnf 1699 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
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