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Mirrors > Home > MPE Home > Th. List > spsd | Structured version Visualization version GIF version |
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 2176 | . 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 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-12 2171 |
This theorem depends on definitions: df-bi 206 df-ex 1782 |
This theorem is referenced by: axc11v 2255 axc11rv 2256 equs5av 2270 equvel 2455 nfsb4t 2498 dfmoeu 2530 moexexlem 2622 2eu6 2652 ab0OLD 4375 zorn2lem4 10496 zorn2lem5 10497 axpowndlem3 10596 axacndlem5 10608 axc11n11r 35653 wl-equsal1i 36504 axc5c4c711 43248 |
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