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| Description: Deduction generalizing antecedent. (Contributed by NM, 17-Aug-1994.) | 
| Ref | Expression | 
|---|---|
| spsd.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) | 
| Ref | Expression | 
|---|---|
| spsd | ⊢ (𝜑 → (∀𝑥𝜓 → 𝜒)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | sp 2183 | . 2 ⊢ (∀𝑥𝜓 → 𝜓) | |
| 2 | spsd.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 3 | 1, 2 | syl5 34 | 1 ⊢ (𝜑 → (∀𝑥𝜓 → 𝜒)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∀wal 1538 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-12 2177 | 
| This theorem depends on definitions: df-bi 207 df-ex 1780 | 
| This theorem is referenced by: axc11v 2264 axc11rv 2265 equs5av 2277 equvel 2461 nfsb4t 2504 dfmoeu 2536 moexexlem 2626 2eu6 2657 zorn2lem4 10539 zorn2lem5 10540 axpowndlem3 10639 axacndlem5 10651 axc11n11r 36684 wl-equsal1i 37545 axc5c4c711 44420 | 
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