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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > sps-o | Structured version Visualization version GIF version |
Description: Generalization of antecedent. (Contributed by NM, 5-Jan-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sps-o.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
sps-o | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-c5 33186 | . 2 ⊢ (∀𝑥𝜑 → 𝜑) | |
2 | sps-o.1 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-c5 33186 |
This theorem is referenced by: axc5c711toc7 33223 axc11n-16 33241 ax12eq 33244 ax12el 33245 ax12inda 33251 ax12v2-o 33252 axc11-o 33254 |
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