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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 38886. (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 38899 | . 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) | |
| 2 | axc4i-o.1 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) | |
| 3 | 1, 2 | alrimih 1823 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∀wal 1537 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-c5 38885 ax-c4 38886 ax-c7 38887 | 
| This theorem is referenced by: hbae-o 38905 aev-o 38933 axc11n-16 38940 ax12indalem 38947 ax12inda2ALT 38948 | 
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