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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax6er | Structured version Visualization version GIF version |
Description: Commuted form of ax6e 2383. (Could be placed right after ax6e 2383). (Contributed by BJ, 15-Sep-2018.) |
Ref | Expression |
---|---|
ax6er | ⊢ ∃𝑥 𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax6e 2383 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
2 | equcomi 2020 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
3 | 1, 2 | eximii 1839 | 1 ⊢ ∃𝑥 𝑦 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-12 2171 ax-13 2372 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1783 |
This theorem is referenced by: exlimiieq2 35005 |
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