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Mirrors > Home > MPE Home > Th. List > hbnaes | Structured version Visualization version GIF version |
Description: Rule that applies hbnae 2440 to antecedent. Usage of this theorem is discouraged because it depends on ax-13 2380. (Contributed by NM, 15-May-1993.) (New usage is discouraged.) |
Ref | Expression |
---|---|
hbnaes.1 | ⊢ (∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦 → 𝜑) |
Ref | Expression |
---|---|
hbnaes | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbnae 2440 | . 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 1535 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-10 2141 ax-11 2158 ax-12 2178 ax-13 2380 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-tru 1540 df-ex 1778 df-nf 1782 |
This theorem is referenced by: (None) |
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