Theorem 2sp 2191

Description: A double specialization (see sp 2188). 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 2188	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2190	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

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 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-12 2182

This theorem depends on definitions:  df-bi 207  df-ex 1781

This theorem is referenced by:  cbv1h  2407  csbie2t  3884  copsex2t  5437  fprlem1  8239  frrlem15  9661  fundmpss  35883  bj-cbv1hv  36913  ax11-pm  36949  mbfresfi  37779  cotrintab  43771  pm14.123b  44583  ich2exprop  47633  ichnreuop  47634  ichreuopeq  47635