Theorem 2sp 2228

Description: A double specialization (see sp 2225). Another double specialization, closer to PM*11.1, is 2stdpc4 2108. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2225	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2227	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1565

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-12 2219

This theorem depends on definitions:  df-bi 210  df-ex 1807

This theorem is referenced by:  cbv1h  2443  csbie2t  3899  copsex2t  5473  fprlem1  8293  frrlem15  9725  fundmpss  36154  bj-cbv1hv  37316  ax11-pm  37352  mbfresfi  38200  cotrintab  44225  pm14.123b  45021  ich2exprop  48102  ichnreuop  48103  ichreuopeq  48104