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| 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 1910, ax-6 1967, ax-7 2007, ax-10 2141, ax-12 2177. (Revised by Wolf Lammen, 8-Jan-2018.) | 
| Ref | Expression | 
|---|---|
| excomim | ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | excom 2162 | . 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑) | |
| 2 | 1 | biimpi 216 | 1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∃wex 1779 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-11 2157 | 
| This theorem depends on definitions: df-bi 207 df-ex 1780 | 
| This theorem is referenced by: 2euswapv 2630 2euswap 2645 relopabi 5832 lfuhgr3 35125 umgr2cycl 35146 ax6e2eq 44577 ax6e2nd 44578 ax6e2eqVD 44927 ax6e2ndVD 44928 ax6e2ndALT 44950 | 
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