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Mirrors > Home > MPE Home > Th. List > exbi | Structured version Visualization version GIF version |
Description: Theorem 19.18 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
exbi | ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓)) | |
2 | 1 | alexbii 1829 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 ∀wal 1531 ∃wex 1776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 |
This theorem depends on definitions: df-bi 209 df-ex 1777 |
This theorem is referenced by: exbii 1844 nfbiit 1847 19.19 2227 eubi 2665 bj-2exbi 33944 bj-3exbi 33945 bj-hbyfrbi 33959 2exbi 40705 rexbidar 40771 onfrALTlem1VD 41217 csbxpgVD 41221 csbrngVD 41223 csbunigVD 41225 e2ebindVD 41239 e2ebindALT 41256 |
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