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Mirrors > Home > MPE Home > Th. List > 3exbidv | Structured version Visualization version GIF version |
Description: Formula-building rule for three existential quantifiers (deduction rule). (Contributed by NM, 1-May-1995.) |
Ref | Expression |
---|---|
3exbidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
3exbidv | ⊢ (𝜑 → (∃𝑥∃𝑦∃𝑧𝜓 ↔ ∃𝑥∃𝑦∃𝑧𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3exbidv.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
2 | 1 | exbidv 1837 | . 2 ⊢ (𝜑 → (∃𝑧𝜓 ↔ ∃𝑧𝜒)) |
3 | 2 | 2exbidv 1839 | 1 ⊢ (𝜑 → (∃𝑥∃𝑦∃𝑧𝜓 ↔ ∃𝑥∃𝑦∃𝑧𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 ∃wex 1695 |
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 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: ceqsex6v 3221 euotd 4900 oprabid 6576 eloprabga 6645 eloprabi 7121 bnj981 30274 |
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