Theorem 2sp 2181

Description: A double specialization (see sp 2178). Another double specialization, closer to PM*11.1, is 2stdpc4 2074. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2178	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2180	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1537

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-12 2173

This theorem depends on definitions:  df-bi 206  df-ex 1784

This theorem is referenced by:  cbv1h  2405  csbie2t  3869  copsex2t  5400  fprlem1  8087  wfrlem5OLD  8115  frrlem15  9446  fundmpss  33646  bj-cbv1hv  34905  ax11-pm  34942  mbfresfi  35750  cotrintab  41111  pm14.123b  41933  ich2exprop  44811  ichnreuop  44812  ichreuopeq  44813