![]() |
Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > axc4i-o | Structured version Visualization version GIF version |
Description: Inference version of ax-c4 38582. (Contributed by NM, 3-Jan-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axc4i-o.1 | ⊢ (∀𝑥𝜑 → 𝜓) |
Ref | Expression |
---|---|
axc4i-o | ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1-o 38595 | . 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) | |
2 | axc4i-o.1 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) | |
3 | 1, 2 | alrimih 1819 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1532 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-c5 38581 ax-c4 38582 ax-c7 38583 |
This theorem is referenced by: hbae-o 38601 aev-o 38629 axc11n-16 38636 ax12indalem 38643 ax12inda2ALT 38644 |
Copyright terms: Public domain | W3C validator |