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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm11.7 | Structured version Visualization version GIF version |
Description: Theorem *11.7 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.) |
Ref | Expression |
---|---|
pm11.7 | ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜑) ↔ ∃𝑥∃𝑦𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oridm 901 | . 2 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑) | |
2 | 1 | 2exbii 1848 | 1 ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜑) ↔ ∃𝑥∃𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∨ wo 843 ∃wex 1779 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 |
This theorem depends on definitions: df-bi 209 df-or 844 df-ex 1780 |
This theorem is referenced by: (None) |
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