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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 2312 using ax-c11 33190. (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 33206 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
2 | dral2-o.1 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
3 | 1, 2 | albidh 1780 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑧𝜑 ↔ ∀𝑧𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-11 2021 ax-c5 33186 ax-c4 33187 ax-c7 33188 ax-c10 33189 ax-c11 33190 ax-c9 33193 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 |
This theorem is referenced by: ax12eq 33244 ax12el 33245 ax12indalem 33248 ax12inda2ALT 33249 |
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