Theorem 2sp 2220

Description: A double specialization (see sp 2217). Another double specialization, closer to PM*11.1, is 2stdpc4 2100. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2217	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2219	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1557

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-12 2211

This theorem depends on definitions:  df-bi 209  df-ex 1799

This theorem is referenced by:  cbv1h  2435  csbie2t  3888  copsex2t  5458  fprlem1  8275  frrlem15  9709  fundmpss  36078  bj-cbv1hv  37242  ax11-pm  37278  mbfresfi  38126  cotrintab  44151  pm14.123b  44963  ich2exprop  48038  ichnreuop  48039  ichreuopeq  48040