Theorem 2sp 2180

Description: A double specialization (see sp 2177). 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 2177	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2179	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-12 2172

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by:  cbv1h  2405  csbie2t  3935  copsex2t  5493  fprlem1  8285  wfrlem5OLD  8313  frrlem15  9752  fundmpss  34738  bj-cbv1hv  35674  ax11-pm  35710  mbfresfi  36534  cotrintab  42365  pm14.123b  43185  ich2exprop  46139  ichnreuop  46140  ichreuopeq  46141