Theorem imim2i 12

Description: Inference adding common antecedents in an implication. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
imim2i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
imim2i	⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

Proof of Theorem imim2i

Step	Hyp	Ref	Expression
1		imim2i.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	a1i 9	. 2 ⊢ (𝜒 → (𝜑 → 𝜓))
3	2	a2i 11	1 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  imim12i  59  imim3i  61  imim21b  251  jcab  598  pm4.78i  777  pm3.48  780  con1dc  851  jadc  858  pm5.6r  922  exbir  1429  19.21h  1550  nford  1560  19.21ht  1574  exim  1592  i19.24  1632  equsexd  1722  equvini  1751  nfexd  1754  sbimi  1757  sbcof2  1803  nfsb2or  1830  mopick  2097  r19.32r  2616  r19.36av  2621  ceqsalt  2756  vtoclgft  2780  spcgft  2807  spcegft  2809  elab3gf  2880  mo2icl  2909  euind  2917  reu6  2919  reuind  2935  sbciegft  2985  ssddif  3361  dfiin2g  3906  invdisj  3983  ordunisuc2r  4498  fnoprabg  5954  caucvgsr  7764  rexanre  11184  tgcnp  13003  lmcvg  13011  elabgft1  13813  bj-nntrans  13986