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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-axc16g16 | Structured version Visualization version GIF version |
Description: Proof of axc16g 2243 from { ax-1 6-- ax-7 2003, axc16 2244 }. (Contributed by BJ, 6-Jul-2021.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-axc16g16 | ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑧𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aevlem 2050 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧 𝑧 = 𝑡) | |
2 | axc16 2244 | . 2 ⊢ (∀𝑧 𝑧 = 𝑡 → (𝜑 → ∀𝑧𝜑)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑧𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-12 2163 |
This theorem depends on definitions: df-bi 206 df-an 396 df-ex 1774 |
This theorem is referenced by: (None) |
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