Theorem 2sp 2183

Description: A double specialization (see sp 2180). Another double specialization, closer to PM*11.1, is 2stdpc4 2075. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2180	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2182	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1536

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 1911  ax-6 1970  ax-7 2015  ax-12 2175

This theorem depends on definitions:  df-bi 210  df-ex 1782

This theorem is referenced by:  cbv1h  2414  csbie2t  3866  copsex2t  5348  wfrlem5  7942  fundmpss  33122  fprlem1  33250  frrlem15  33255  bj-cbv1hv  34233  ax11-pm  34270  mbfresfi  35103  cotrintab  40314  pm14.123b  41130  ich2exprop  43988  ichnreuop  43989  ichreuopeq  43990