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Mirrors > Home > MPE Home > Th. List > axc4i | Structured version Visualization version GIF version |
Description: Inference version of axc4 2273. (Contributed by NM, 3-Jan-1993.) |
Ref | Expression |
---|---|
axc4i.1 | ⊢ (∀𝑥𝜑 → 𝜓) |
Ref | Expression |
---|---|
axc4i | ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2173 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | axc4i.1 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) | |
3 | 1, 2 | alrimi 2225 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1626 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1867 ax-4 1882 ax-5 1984 ax-6 2050 ax-7 2086 ax-10 2164 ax-12 2192 |
This theorem depends on definitions: df-bi 197 df-or 384 df-ex 1850 df-nf 1855 |
This theorem is referenced by: hbae 2453 hbsb2 2492 hbsb2a 2494 hbsb2e 2496 reu6 3532 axunndlem1 9605 axacndlem3 9619 axacndlem5 9621 axacnd 9622 bj-nfs1t 33016 bj-hbs1 33060 bj-hbsb2av 33062 bj-hbaeb2 33107 wl-hbae1 33612 frege93 38748 pm11.57 39087 pm11.59 39089 axc5c4c711toc7 39103 axc11next 39105 hbalg 39269 ax6e2eq 39271 ax6e2eqVD 39638 |
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