Theorem 2sp 2183

Description: A double specialization (see sp 2180). Another double specialization, closer to PM*11.1, is 2stdpc4 2067. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2180	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2182	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1534

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-12 2174

This theorem depends on definitions:  df-bi 207  df-ex 1776

This theorem is referenced by:  cbv1h  2407  csbie2t  3948  copsex2t  5502  fprlem1  8323  wfrlem5OLD  8351  frrlem15  9794  fundmpss  35747  bj-cbv1hv  36778  ax11-pm  36814  mbfresfi  37652  cotrintab  43603  pm14.123b  44421  ich2exprop  47395  ichnreuop  47396  ichreuopeq  47397