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Mirrors > Home > MPE Home > Th. List > hbnaes | Structured version Visualization version GIF version |
Description: Rule that applies hbnae 2317 to antecedent. (Contributed by NM, 15-May-1993.) |
Ref | Expression |
---|---|
hbnaes.1 | ⊢ (∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦 → 𝜑) |
Ref | Expression |
---|---|
hbnaes | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbnae 2317 | . 2 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦) | |
2 | hbnaes.1 | . 2 ⊢ (∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦 → 𝜑) | |
3 | 1, 2 | syl 17 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1481 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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