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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dral2-o | Structured version Visualization version GIF version |
Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). Version of dral2 2429 using ax-c11 38260. (Contributed by NM, 27-Feb-2005.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dral2-o.1 | ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
dral2-o | ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑧𝜑 ↔ ∀𝑧𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbae-o 38276 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
2 | dral2-o.1 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
3 | 1, 2 | albidh 1861 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑧𝜑 ↔ ∀𝑧𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∀wal 1531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-11 2146 ax-c5 38256 ax-c4 38257 ax-c7 38258 ax-c10 38259 ax-c11 38260 ax-c9 38263 |
This theorem depends on definitions: df-bi 206 df-an 396 df-ex 1774 |
This theorem is referenced by: ax12eq 38314 ax12el 38315 ax12indalem 38318 ax12inda2ALT 38319 |
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