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Mirrors > Home > MPE Home > Th. List > ax11w | Structured version Visualization version GIF version |
Description: Weak version of ax-11 2155 from which we can prove any ax-11 2155 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. Unlike ax-11 2155, this theorem requires that 𝑥 and 𝑦 be distinct i.e. are not bundled. It is an alias of alcomimw 2040 introduced for labeling consistency. (Contributed by NM, 10-Apr-2017.) Use alcomimw 2040 instead. (New usage is discouraged.) |
Ref | Expression |
---|---|
ax11w.1 | ⊢ (𝑦 = 𝑧 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
ax11w | ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑦∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax11w.1 | . 2 ⊢ (𝑦 = 𝑧 → (𝜑 ↔ 𝜓)) | |
2 | 1 | alcomimw 2040 | 1 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑦∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 206 ∀wal 1535 |
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 1908 ax-6 1965 ax-7 2005 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1777 |
This theorem is referenced by: (None) |
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