Theorem 2sp 2187

Description: A double specialization (see sp 2184). Another double specialization, closer to PM*11.1, is 2stdpc4 2071. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2184	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2186	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

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 2008  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-ex 1780

This theorem is referenced by:  cbv1h  2403  csbie2t  3900  copsex2t  5452  fprlem1  8279  frrlem15  9710  fundmpss  35754  bj-cbv1hv  36784  ax11-pm  36820  mbfresfi  37660  cotrintab  43603  pm14.123b  44415  ich2exprop  47472  ichnreuop  47473  ichreuopeq  47474