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Mirrors > Home > MPE Home > Th. List > axc16 | Structured version Visualization version GIF version |
Description: Proof of older axiom ax-c16 34650. (Contributed by NM, 8-Nov-2006.) (Revised by NM, 22-Sep-2017.) |
Ref | Expression |
---|---|
axc16 | ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc16g 2269 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 → ∀𝑥𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1618 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1859 ax-4 1874 ax-5 1976 ax-6 2042 ax-7 2078 ax-12 2184 |
This theorem depends on definitions: df-bi 197 df-an 385 df-ex 1842 |
This theorem is referenced by: axc16nfOLD 2296 ax12vALT 2553 hbs1 2561 exists2 2688 bj-ax6elem1 32928 axc11n11r 32950 bj-axc16g16 32951 |
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