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Mirrors > Home > MPE Home > Th. List > axc16nfALT | Structured version Visualization version GIF version |
Description: Alternate proof of axc16nf 2264, shorter but requiring ax-11 2161 and ax-13 2390. (Contributed by Mario Carneiro, 7-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axc16nfALT | ⊢ (∀𝑥 𝑥 = 𝑦 → Ⅎ𝑧𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfae 2455 | . 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦 | |
2 | axc16g 2261 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑧𝜑)) | |
3 | 1, 2 | nf5d 2292 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → Ⅎ𝑧𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1535 Ⅎwnf 1784 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-11 2161 ax-12 2177 ax-13 2390 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 |
This theorem is referenced by: (None) |
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