Theorem 2sp 2223

Description: A double specialization (see sp 2220). 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 2220	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2222	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 2213

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

This theorem is used by:  cbv1h  2435  csbie2t  3885  copsex2t  5464  fprlem1  8311  frrlem15  9754  fundmpss  36511  bj-cbv1hv  37688  ax11-pm  37724  mbfresfi  38564  cotrintab  44599  pm14.123b  45395  ich2exprop  48522  ichnreuop  48523  ichreuopeq  48524