Theorem 2sp 2222

Description: A double specialization (see sp 2219). Another double specialization, closer to PM*11.1, is 2stdpc4 2104. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2219	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2221	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1568

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-12 2213

This theorem depends on definitions:  df-bi 210  df-ex 1810

This theorem is referenced by:  cbv1h  2437  csbie2t  3892  copsex2t  5477  fprlem1  8298  frrlem15  9730  fundmpss  36240  bj-cbv1hv  37412  ax11-pm  37448  mbfresfi  38298  cotrintab  44323  pm14.123b  45119  ich2exprop  48203  ichnreuop  48204  ichreuopeq  48205