Theorem 2sp 2225

Description: A double specialization (see sp 2222). Another double specialization, closer to PM*11.1, is 2stdpc4 2107. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2222	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2224	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  cbv1h  2439  csbie2t  3892  copsex2t  5477  fprlem1  8299  frrlem15  9732  fundmpss  36272  bj-cbv1hv  37464  ax11-pm  37500  mbfresfi  38350  cotrintab  44373  pm14.123b  45169  ich2exprop  48253  ichnreuop  48254  ichreuopeq  48255