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Mirrors > Home > MPE Home > Th. List > axc4i | Structured version Visualization version GIF version |
Description: Inference version of axc4 2314. (Contributed by NM, 3-Jan-1993.) |
Ref | Expression |
---|---|
axc4i.1 | ⊢ (∀𝑥𝜑 → 𝜓) |
Ref | Expression |
---|---|
axc4i | ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2148 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | axc4i.1 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) | |
3 | 1, 2 | alrimi 2206 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1539 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-10 2137 ax-12 2171 |
This theorem depends on definitions: df-bi 206 df-or 846 df-ex 1782 df-nf 1786 |
This theorem is referenced by: hbae 2429 hbsb2 2480 hbsb2a 2482 hbsb2e 2484 nfabdwOLD 2926 reu6 3718 ralidm 4505 axunndlem1 10572 axacndlem3 10586 axacndlem5 10588 axacnd 10589 bj-nfs1t 35470 bj-hbs1 35492 bj-hbsb2av 35494 bj-hbaeb2 35498 wl-hbae1 36190 frege93 42476 spALT 42722 pm11.57 42917 pm11.59 42919 axc5c4c711toc7 42932 axc11next 42934 hbalg 43085 ax6e2eq 43087 ax6e2eqVD 43437 ichnfimlem 45901 |
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