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Mirrors > Home > MPE Home > Th. List > Mathboxes > axc4i-o | Structured version Visualization version GIF version |
Description: Inference version of ax-c4 36543. (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 36556 | . 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) | |
2 | axc4i-o.1 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) | |
3 | 1, 2 | alrimih 1830 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-c5 36542 ax-c4 36543 ax-c7 36544 |
This theorem is referenced by: hbae-o 36562 aev-o 36590 axc11n-16 36597 ax12indalem 36604 ax12inda2ALT 36605 |
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