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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 1813 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1536 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-gen 1797 ax-4 1811 |
This theorem is referenced by: 19.38 1840 stdpc4 2073 ax12dgen 2135 ax12 2434 sb4a 2498 stdpc4ALT 2566 alral 3122 hbimtg 33164 bj-axdd2 34039 bj-ax12v3ALT 34133 bj-equsal1t 34260 |
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