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Mirrors > Home > MPE Home > Th. List > excomim | Structured version Visualization version GIF version |
Description: One direction of Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) Remove dependencies on ax-5 1839, ax-6 1888, ax-7 1935, ax-10 2019, ax-12 2047. (Revised by Wolf Lammen, 8-Jan-2018.) |
Ref | Expression |
---|---|
excomim | ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 2042 | . 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑) | |
2 | 1 | biimpi 206 | 1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-11 2034 |
This theorem depends on definitions: df-bi 197 df-ex 1705 |
This theorem is referenced by: 2euswap 2548 relopabi 5245 ax6e2eq 38773 ax6e2nd 38774 ax6e2eqVD 39143 ax6e2ndVD 39144 ax6e2ndALT 39166 |
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