Theorem 2sp 2179

Description: A double specialization (see sp 2176). Another double specialization, closer to PM*11.1, is 2stdpc4 2073. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2176	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2178	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 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171

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

This theorem is referenced by:  cbv1h  2405  csbie2t  3873  copsex2t  5406  fprlem1  8116  wfrlem5OLD  8144  frrlem15  9515  fundmpss  33740  bj-cbv1hv  34978  ax11-pm  35015  mbfresfi  35823  cotrintab  41222  pm14.123b  42044  ich2exprop  44923  ichnreuop  44924  ichreuopeq  44925