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| Description: Theorem 19.35 of [Margaris] p. 90. This theorem is useful for moving an implication (in the form of the right-hand side) into the scope of a single existential quantifier. |
| Ref | Expression |
|---|---|
| 19.35 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.26 1703 |
. . . 4
| |
| 2 | annim 365 |
. . . . 5
| |
| 3 | 2 | albii 1635 |
. . . 4
|
| 4 | df-an 339 |
. . . 4
| |
| 5 | 1, 3, 4 | 3bitr3i 293 |
. . 3
|
| 6 | 5 | con2bii 335 |
. 2
|
| 7 | df-ex 1616 |
. . 3
| |
| 8 | 7 | imbi2i 297 |
. 2
|
| 9 | df-ex 1616 |
. 2
| |
| 10 | 6, 8, 9 | 3bitr4ri 296 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: 19.35i 1713 19.35ri 1714 19.36 1715 19.37 1717 19.39 1719 19.24 1720 19.25 1721 sbequi 1874 grothprim 11012 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-gen 1593 ax-4 1608 ax-5o 1610 |
| This theorem depends on definitions: df-bi 220 df-an 339 df-ex 1616 |