Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 1911, ax-6 1970, ax-7 2015, ax-10 2145, ax-12 2177. (Revised by Wolf Lammen, 8-Jan-2018.) |
Ref | Expression |
---|---|
excomim | ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 2169 | . 2 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑦∃𝑥𝜑) | |
2 | 1 | biimpi 218 | 1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-11 2161 |
This theorem depends on definitions: df-bi 209 df-ex 1781 |
This theorem is referenced by: 2euswapv 2715 2euswap 2730 relopabi 5694 lfuhgr3 32366 umgr2cycl 32388 ax6e2eq 40911 ax6e2nd 40912 ax6e2eqVD 41261 ax6e2ndVD 41262 ax6e2ndALT 41284 |
Copyright terms: Public domain | W3C validator |