| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > 2sp | Structured version Visualization version GIF version | ||
| Description: A double specialization (see sp 2183). Another double specialization, closer to PM*11.1, is 2stdpc4 2070. (Contributed by BJ, 15-Sep-2018.) |
| Ref | Expression |
|---|---|
| 2sp | ⊢ (∀𝑥∀𝑦𝜑 → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sp 2183 | . 2 ⊢ (∀𝑦𝜑 → 𝜑) | |
| 2 | 1 | sps 2185 | 1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∀wal 1538 |
| 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-5 1910 ax-6 1967 ax-7 2007 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-ex 1780 |
| This theorem is referenced by: cbv1h 2410 csbie2t 3937 copsex2t 5497 fprlem1 8325 wfrlem5OLD 8353 frrlem15 9797 fundmpss 35767 bj-cbv1hv 36797 ax11-pm 36833 mbfresfi 37673 cotrintab 43627 pm14.123b 44445 ich2exprop 47458 ichnreuop 47459 ichreuopeq 47460 |
| Copyright terms: Public domain | W3C validator |