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Mirrors > Home > MPE Home > Th. List > ax10w | Structured version Visualization version GIF version |
Description: Weak version of ax-10 2141 from which we can prove any ax-10 2141 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. It is an alias of hbn1w 2049 introduced for labeling consistency. (Contributed by NM, 9-Apr-2017.) Use hbn1w 2049 instead. (New usage is discouraged.) |
Ref | Expression |
---|---|
ax10w.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
ax10w | ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax10w.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
2 | 1 | hbn1w 2049 | 1 ⊢ (¬ ∀𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 208 ∀wal 1531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 |
This theorem is referenced by: (None) |
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