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Mirrors > Home > MPE Home > Th. List > 2sp | Structured version Visualization version GIF version |
Description: A double specialization (see sp 2176). Another double specialization, closer to PM*11.1, is 2stdpc4 2073. (Contributed by BJ, 15-Sep-2018.) |
Ref | Expression |
---|---|
2sp | ⊢ (∀𝑥∀𝑦𝜑 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 2176 | . 2 ⊢ (∀𝑦𝜑 → 𝜑) | |
2 | 1 | sps 2178 | 1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1539 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-12 2171 |
This theorem depends on definitions: df-bi 206 df-ex 1782 |
This theorem is referenced by: cbv1h 2403 csbie2t 3896 copsex2t 5449 fprlem1 8231 wfrlem5OLD 8259 frrlem15 9693 fundmpss 34341 bj-cbv1hv 35261 ax11-pm 35297 mbfresfi 36124 cotrintab 41876 pm14.123b 42696 ich2exprop 45653 ichnreuop 45654 ichreuopeq 45655 |
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