Theorem 2sp 2189

Description: A double specialization (see sp 2186). Another double specialization, closer to PM*11.1, is 2stdpc4 2073. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2186	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2188	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 2180

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

This theorem is referenced by:  cbv1h  2405  csbie2t  3883  copsex2t  5427  fprlem1  8225  frrlem15  9645  fundmpss  35803  bj-cbv1hv  36830  ax11-pm  36866  mbfresfi  37706  cotrintab  43647  pm14.123b  44459  ich2exprop  47502  ichnreuop  47503  ichreuopeq  47504