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Mirrors > Home > ILE Home > Th. List > excom | GIF version |
Description: Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
excom | ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excomim 1663 | . 2 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) | |
2 | excomim 1663 | . 2 ⊢ (∃𝑦∃𝑥𝜑 → ∃𝑥∃𝑦𝜑) | |
3 | 1, 2 | impbii 126 | 1 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 105 ∃wex 1492 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: excom13 1689 exrot3 1690 ee4anv 1934 sbexyz 2003 2exsb 2009 2euex 2113 2exeu 2118 2eu4 2119 rexcomf 2639 gencbvex 2783 euxfr2dc 2922 euind 2924 sbccomlem 3037 opelopabsbALT 4259 uniuni 4451 elvvv 4689 elco 4793 dmuni 4837 dm0rn0 4844 dmmrnm 4846 dmcosseq 4898 elres 4943 rnco 5135 coass 5147 oprabid 5906 dfoprab2 5921 opabex3d 6121 opabex3 6122 cnvoprab 6234 domen 6750 xpassen 6829 prarloc 7501 fisumcom2 11441 fprodcom2fi 11629 |
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