Theorem 2sp 2194

Description: A double specialization (see sp 2191). Another double specialization, closer to PM*11.1, is 2stdpc4 2076. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2191	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2193	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 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-12 2185

This theorem depends on definitions:  df-bi 207  df-ex 1782

This theorem is referenced by:  cbv1h  2410  csbie2t  3889  copsex2t  5448  fprlem1  8252  frrlem15  9681  fundmpss  35980  bj-cbv1hv  37041  ax11-pm  37077  mbfresfi  37914  cotrintab  43967  pm14.123b  44779  ich2exprop  47828  ichnreuop  47829  ichreuopeq  47830