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Mirrors > Home > MPE Home > Th. List > ala1 | Structured version Visualization version GIF version |
Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
ala1 | ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 ⊢ (𝜑 → (𝜓 → 𝜑)) | |
2 | 1 | alimi 1806 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1532 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-gen 1790 ax-4 1804 |
This theorem is referenced by: 19.38 1834 stdpc4 2064 ax12dgen 2123 ax12 2418 sb4a 2475 alral 3071 hbimtg 35396 bj-axdd2 36063 bj-ax12v3ALT 36157 bj-equsal1t 36293 |
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